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A092815 Schmidt's problem sum for r = 5.

%I A092815 #21 Feb 16 2025 08:32:53
%S A092815 1,33,15553,27748833,61371200001,155741521320033,487874692844719489,
%T A092815 1730097641006678817249,6559621957318406477234689,
%U A092815 26511434186466256434467280033,113203209912753307355868621335553,503697803885283278416185835107071649,2318764463485777975432760948801307487809
%N A092815 Schmidt's problem sum for r = 5.
%H A092815 Vincenzo Librandi, <a href="/A092815/b092815.txt">Table of n, a(n) for n = 0..200</a>
%H A092815 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Asymptotic of generalized Apery sequences with powers of binomial coefficients</a>, Nov 04 2012
%H A092815 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SchmidtsProblem.html">Schmidt's Problem</a>
%F A092815 a(n) = sum(k=0..n, binomial(n,k)^5 * binomial(n+k,k)^5 ). - corrected by _Vaclav Kotesovec_, Nov 04 2012
%F A092815 a(n) ~ (1+sqrt(2))^(5*(2n+1))/(2^(13/4)*(Pi*n)^(9/2)*sqrt(5)). - _Vaclav Kotesovec_, Nov 04 2012
%t A092815 Table[Sum[Binomial[n, k]^5 Binomial[n+k, k]^5, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Nov 04 2012 *)
%o A092815 (PARI) a(n)=sum(k=0,n,binomial(n,k)^5*binomial(n+k,k)^5); \\ _Joerg Arndt_, May 11 2013
%Y A092815 Cf. A001850, A005259, A092813, A092814, A218689.
%K A092815 nonn
%O A092815 0,2
%A A092815 _Eric W. Weisstein_, Mar 06 2004
%E A092815 Prepended missing a(0)=1, _Joerg Arndt_, May 11 2013