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A092814
Schmidt's problem sum for r = 4.
6
1, 17, 2593, 990737, 473940001, 261852948017, 166225611652129, 115586046457265681, 85467827222155042849, 66421846251482628852017, 53755021948680412765238593, 44947131400352317819689905201, 38613445585740736549461528111649, 33942058336306457714420306982430001
OFFSET
0,2
LINKS
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