OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Vaclav 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)^4 * binomial(n+k,k)^4 ).
a(n) ~ (1+sqrt(2))^(4*(2n+1))/(2^(15/4)*(Pi*n)^(7/2)). - Vaclav Kotesovec, Nov 04 2012
MATHEMATICA
Table[Sum[Binomial[n, k]^4 Binomial[n+k, k]^4, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 04 2012 *)
a[k_]:= HypergeometricPFQ[{-k, -k, -k, -k, 1+k, 1+k, 1+k, 1+k}, {1, 1, 1, 1, 1, 1, 1}, 1]
Table[ a[k], {k, 0, 20}] (* Gerry Martens, Sep 26 2022 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(n, k)^4*binomial(n+k, k)^4); \\ Joerg Arndt, May 11 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Mar 06 2004
EXTENSIONS
Prepended missing a(0)=1, Joerg Arndt, May 11 2013
STATUS
approved