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A092815 Schmidt's problem sum for r = 5. 6
1, 33, 15553, 27748833, 61371200001, 155741521320033, 487874692844719489, 1730097641006678817249, 6559621957318406477234689, 26511434186466256434467280033, 113203209912753307355868621335553, 503697803885283278416185835107071649, 2318764463485777975432760948801307487809 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

V. Kotesovec, Asymptotic of generalized Apery sequences with powers of binomial coefficients, Nov 04 2012

Eric Weisstein's World of Mathematics, Schmidt's Problem

FORMULA

a(n) = sum(k=0..n, binomial(n,k)^5 * binomial(n+k,k)^5 ). - corrected by Vaclav Kotesovec, Nov 04 2012

a(n) ~ (1+sqrt(2))^(5*(2n+1))/(2^(13/4)*(Pi*n)^(9/2)*sqrt(5)). - Vaclav Kotesovec, Nov 04 2012

MATHEMATICA

Table[Sum[Binomial[n, k]^5 Binomial[n+k, k]^5, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 04 2012 *)

PROG

(PARI) a(n)=sum(k=0, n, binomial(n, k)^5*binomial(n+k, k)^5); \\ Joerg Arndt, May 11 2013

CROSSREFS

Cf. A001850, A005259, A092813, A092814, A218689.

Sequence in context: A232148 A229845 A232306 * A230673 A238565 A232456

Adjacent sequences:  A092812 A092813 A092814 * A092816 A092817 A092818

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Mar 06 2004

EXTENSIONS

Prepended missing a(0)=1, Joerg Arndt, May 11 2013

STATUS

approved

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Last modified October 25 11:29 EDT 2021. Contains 348251 sequences. (Running on oeis4.)