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A295612 a(n) = Sum_{k=0..n} binomial(n+k,k)^k. 2
1, 3, 40, 8105, 24053106, 1016507243472, 622366942086680904, 5608321882919220905812521, 752711651805019773658037206391596, 1518219710649896586598445898967340890577318, 46343146356260529633020448755386347142785083052620084 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..41

Eric Weisstein's World of Mathematics, Binomial Sums

FORMULA

a(n) = Sum_{k=0..n} A046899(n,k)^k.

a(n) ~ 2^(2*n^2) / (exp(1/8) * Pi^(n/2) * n^(n/2)). - Vaclav Kotesovec, Nov 25 2017

MATHEMATICA

Table[Sum[Binomial[n + k, k]^k, {k, 0, n}], {n, 0, 10}]

Table[Sum[((n + k)!/(n! k!))^k, {k, 0, n}], {n, 0, 10}]

PROG

(PARI) a(n) = sum(k=0, n, binomial(n+k, k)^k); \\ Michel Marcus, Nov 25 2017

CROSSREFS

Cf. A001700, A046899, A112028, A112029, A167008, A219562, A219563, A219564.

Sequence in context: A094330 A110468 A327356 * A286661 A171058 A105906

Adjacent sequences:  A295609 A295610 A295611 * A295613 A295614 A295615

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 24 2017

STATUS

approved

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Last modified September 24 07:28 EDT 2020. Contains 337317 sequences. (Running on oeis4.)