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A234971 Sum_{k=0..n} n^k * binomial(n,k)^4. 3
2, 37, 1000, 38401, 1896876, 112124629, 7679202336, 595411451905, 51348552829300, 4861414171762501, 500163335120177136, 55466421261812540929, 6585829687114412247800, 832587068884779776276661, 111541424966889778569909376, 15771414153994526723881828353 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In general, sum_{k=0..n} n^k * binomial(n,k)^p is asymptotic to (1+n^(1/p))^(n*p+p-1) / sqrt(p * (2*Pi)^(p-1) * n^(p-1/p)).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

V. Kotesovec, Asymptotic of a sums of powers of binomial coefficients * x^k, 2012

FORMULA

a(n) ~ (1+n^(1/4))^(4*n+3) / (4*sqrt(2) * Pi^(3/2) * n^(15/8)).

MATHEMATICA

Table[Sum[n^k*Binomial[n, k]^4, {k, 0, n}], {n, 1, 20}]

CROSSREFS

Cf. A187021, A241247.

Sequence in context: A307318 A058245 A257995 * A139108 A165697 A320994

Adjacent sequences:  A234968 A234969 A234970 * A234972 A234973 A234974

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Apr 19 2014

STATUS

approved

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Last modified November 18 07:22 EST 2019. Contains 329252 sequences. (Running on oeis4.)