A092815 Schmidt's problem sum for r = 5.

1, 33, 15553, 27748833, 61371200001, 155741521320033, 487874692844719489, 1730097641006678817249, 6559621957318406477234689, 26511434186466256434467280033, 113203209912753307355868621335553, 503697803885283278416185835107071649, 2318764463485777975432760948801307487809

Offset: 0

Author

Eric W. Weisstein, Mar 06 2004

Keywords

• nonn

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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

Extensions

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