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A092813
Schmidt's problem sum for r = 3.
6
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
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 06 2004
EXTENSIONS
Prepended missing a(0)=1, Joerg Arndt, May 11 2013
STATUS
approved