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A242446 a(n) = Sum_{k=1..n} C(n,k) * k^(2*n). 3
1, 18, 924, 93320, 15609240, 3903974592, 1364509038592, 635177480713344, 379867490829555840, 283825251434680651520, 259092157573229145859584, 283735986144895532781391872, 367138254141051794797009309696, 554136240038549806366753446051840 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Generally, for p>=1, a(n) = Sum_{k=1..n} C(n,k) * k^(p*n) is asymptotic to sqrt(r/(p+r-p*r)) * r^(p*n) * n^(p*n) / (exp(p*n) * (1-r)^n), where r = p/(p+LambertW(p*exp(-p))).

Sum_{k=1..n} (-1)^(n-k) * C(n,k) * k^(p*n) = n! * stirling2(p*n,n).

LINKS

Table of n, a(n) for n=1..14.

FORMULA

a(n) ~ sqrt(r/(2-r)) * r^(2*n) * n^(2*n) / (exp(2*n) * (1-r)^n), where r = 2/(2+LambertW(2*exp(-2))).

MATHEMATICA

Table[Sum[Binomial[n, k]*k^(2*n), {k, 1, n}], {n, 1, 20}]

CROSSREFS

Cf. A007820, A072034, A242449, A256016.

Sequence in context: A215194 A201538 A214160 * A160013 A123786 A333089

Adjacent sequences:  A242443 A242444 A242445 * A242447 A242448 A242449

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, May 14 2014

STATUS

approved

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Last modified June 24 18:46 EDT 2021. Contains 345419 sequences. (Running on oeis4.)