OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..830
FORMULA
a(n) = A005260(n)/(n+1).
a(n) = Sum_{k=0..n} binomial(n,k)^2 * ( binomial(n,k) - binomial(n,k-1) )^2. - Seiichi Manyama, Mar 26 2025
a(n) ~ 2^(4*n + 1/2) / (Pi^(3/2) * n^(5/2)). - Vaclav Kotesovec, Mar 26 2025
MAPLE
a:=n->add(binomial(n, k)^4/(n+1), k=0..n): seq(a(n), n=0..20); # Muniru A Asiru, Jan 22 2019
MATHEMATICA
Table[Sum[Binomial[n, k]^4/(n+1), {k, 0, n}], {n, 0, 20}] (* G. C. Greubel, Jan 22 2019 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)^4)/(n+1)}
(Magma) [(&+[Binomial(n, k)^4/(n+1): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Jan 22 2019
(SageMath) [sum(binomial(n, k)^4/(n+1) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Jan 22 2019
(GAP) List([0..20], n-> Sum([0..n], k-> Binomial(n, k)^4/(n+1) )); # G. C. Greubel, Jan 22 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 27 2010
STATUS
approved