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A342178
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Product of first n central Delannoy numbers.
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0
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1, 3, 39, 2457, 788697, 1327377051, 11931792311439, 580350446236081521, 154215943727867706493809, 225550533306461376412704772467, 1826384842574005591817185497927226551, 82272644789290466599017454496002856892236169
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Product_{k=1..n} A001850(k).
a(n) ~ c * (1 + sqrt(2))^(n*(n+2)) * exp(n/2) / (2^((5*n+1)/4) * Pi^(n/2 + 1/4) * n^((n+1)/2 - 3/(16*sqrt(2)))), where c = 0.9486848745280397752870611535632702994491680306036912732565033220352175749...
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MAPLE
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b:= proc(n) option remember; `if`(n<1, 1,
(3*(2*n-1)*b(n-1) -(n-1)*b(n-2))/n)
end:
a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end:
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MATHEMATICA
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Table[Product[Hypergeometric2F1[-k, k+1, 1, -1], {k, 1, n}], {n, 0, 15}]
FoldList[Times, 1, Table[Hypergeometric2F1[-n, n + 1, 1, -1], {n, 1, 15}]]
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PROG
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(PARI) D(n) = sum(k=0, n, binomial(n, k)*binomial(n+k, k)); \\ A001850
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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