A092813 Schmidt's problem sum for r = 3.

1, 9, 433, 36729, 3824001, 450954009, 58160561761, 7989733343097, 1149808762915201, 171540347534028009, 26338900959100106433, 4140153621102790276137, 663592912043903970182289, 108127319237119098011204937, 17868369859451104998973346433, 2989001418301890511076878884729

Offset

0,2

Comments

Apparently, the diagonal of 1/((1 - x - y)*(1 - z - t)*(1 - u - w) - x*y*z*t*u*w). - Peter Bala, Jun 30 2023

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)^3 * binomial(n+k,k)^3.

a(n) ~ (1+sqrt(2))^(3*(2*n+1))/(2^(9/4)*(Pi*n)^(5/2)*sqrt(3)). - Vaclav Kotesovec, Nov 04 2012

Mathematica

Table[Sum[Binomial[n, k]^3 Binomial[n+k, k]^3, {k, 0, n}], {n, 0, 20}] (*Harvey P. Dale, Apr 26 2011 *)

Prog

(PARI) a(n)=sum(k=0, n, binomial(n, k)^3*binomial(n+k, k)^3); \\ Joerg Arndt, May 11 2013

Crossrefs

Cf. A001850, A005259, A092814, A092815, A218689.

Sequence in context: A160376 A271652 A156092 * A242280 A266294 A273889

Adjacent sequences: A092810 A092811 A092812 * A092814 A092815 A092816

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 06 2004

Extensions

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

Status

approved