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Revision History for A351734

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Showing entries 1-10 | older changes

A351734

Expansion of e.g.f. exp( 3 * x * (exp(x) - 1) ).
(history; published version)

#11 by Michael De Vlieger at Sat May 21 08:41:03 EDT 2022

STATUS

proposed

approved

#10 by Seiichi Manyama at Sat May 21 08:33:21 EDT 2022

STATUS

editing

proposed

#9 by Seiichi Manyama at Fri May 20 13:28:04 EDT 2022

CROSSREFS

Cf. A053490, A351737.

#8 by Seiichi Manyama at Fri May 20 13:27:03 EDT 2022

CROSSREFS

Cf. A052506, A351733.

#7 by Seiichi Manyama at Fri May 20 13:17:25 EDT 2022

CROSSREFS

Cf. A053490.

#6 by Seiichi Manyama at Fri May 20 13:16:44 EDT 2022

DATA

1, 0, 6, 9, 120, 555, 5148, 39711, 378528, 3715011, 39838260, 452684463, 5463506304, 69553644771, 930940368036, 13054086036855, 191222363275968, 2918620069099395, 46309955947643124, 762335523354333855, 12995722456718984160, 229045407317491457763

FORMULA

a(n) = n! * Sum_{k=0..floor(n/2)} 3^k * Stirling2(n-k,k)/(n-k)!.

#5 by Seiichi Manyama at Fri May 20 13:15:36 EDT 2022

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(3*x*(exp(x)-1))))

(PARI) a(n) = n!*sum(k=0, n\2, 3^k*stirling(n-k, k, 2)/(n-k)!);

#4 by Seiichi Manyama at Fri May 20 12:55:45 EDT 2022

NAME

allocated for Seiichi Manyama

Expansion of e.g.f. exp( 3 * x * (exp(x) - 1) ).

DATA

1, 0, 6, 9, 120, 555, 5148, 39711, 378528, 3715011, 39838260, 452684463, 5463506304, 69553644771, 930940368036

OFFSET

0,3

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, May 20 2022

STATUS

approved

editing

#3 by Seiichi Manyama at Fri May 20 12:55:45 EDT 2022

NAME

allocated for Seiichi Manyama

KEYWORD

recycled

allocated

#2 by Andrew Howroyd at Fri May 20 12:15:37 EDT 2022

NAME

allocated for Andrew Howroyd

KEYWORD

allocated

recycled