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#54 by Michael De Vlieger at Sat Jun 08 16:44:59 EDT 2024
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#53 by Stefano Spezia at Sat Jun 08 16:17:22 EDT 2024
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#52 by Jon E. Schoenfield at Sat Jun 08 12:43:43 EDT 2024
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Discussion
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| Sat Jun 08
| 16:17
| Stefano Spezia: For me ok
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#51 by Jon E. Schoenfield at Sat Jun 08 12:43:34 EDT 2024
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| FORMULA
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a(n) = (1/e)*Sum_{k>=0} (3*k)^n/k!, this!. (This is a Dobinski-type formula..)
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Discussion
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| Sat Jun 08
| 12:43
| Jon E. Schoenfield: @All: I edited some of the Formula section entries in an attempt to improve their readability. Do these look okay?
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#50 by Jon E. Schoenfield at Sat Jun 08 12:40:38 EDT 2024
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a(n) = exp(-) = (1/e)*Sum_{k>=0} (3*k)^n/k!, this is a Dobinski-type formula.
O.g.f.: exp(-.: (1/e)*Sum_{k>=0} 1/(k!*(1-3*k*z)).
a(n) is the n-th moment of a discrete, positive weight function w(x) consisting of an infinite comb of Dirac delta functions situated at x=3*k, with k = 0, 1, ..., defined as w(x) = exp(-) = (1/e)*Sum_{k>=0} Dirac(x-3*k)/k!.
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#49 by Jon E. Schoenfield at Sat Jun 08 12:39:14 EDT 2024
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| FORMULA
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a(n) = sum(exp(-1)*Sum_{k>=0, (} (3*k)^n/k!)/exp(1), !, this is a Dobinski-type formula.
O.g.f.: sum(exp(-1)*Sum_{k>=0, } 1/(k!*(1-3*k*z)) )/exp(1).)).
a(n) is the n-th moment of a discrete, positive weight function w(x) consisting of an infinite comb of Dirac delta functions situated at x=3*k, with k = 0, 1, ..., defined as w(x)=sum() = exp(-1)*Sum_{k>=0, } Dirac(x-3*k)/k!)/exp(1).!.
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#48 by Jon E. Schoenfield at Sat Jun 08 12:35:10 EDT 2024
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| NAME
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a(n)=) = 3^n*Bell(n).
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| STATUS
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proposed
editing
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#47 by Robert C. Lyons at Sat Jun 08 12:33:51 EDT 2024
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#46 by Robert C. Lyons at Sat Jun 08 12:33:49 EDT 2024
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| PROG
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.... blist = list(accumulate([b]+blist))
.... b = blist[-1]
.... A247452_list.append(b*n3)
.... n3 *= 3 # Chai Wah Wu, Sep 19 2014
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| STATUS
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approved
editing
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#45 by Charles R Greathouse IV at Thu Sep 08 08:46:09 EDT 2022
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Discussion
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| Thu Sep 08
| 08:46
| OEIS Server: https://oeis.org/edit/global/2944
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