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A371739
a(n) = Sum_{k=0..n} binomial(5*n,k).
3
1, 6, 56, 576, 6196, 68406, 768212, 8731848, 100146724, 1156626990, 13432735556, 156713948672, 1835237017324, 21560768699762, 253994850228896, 2999267652451776, 35490014668470052, 420718526924212654, 4995548847105422048, 59402743684137281920
OFFSET
0,2
FORMULA
a(n) = [x^n] 1/((1-2*x) * (1-x)^(4*n)).
a(n) ~ 5^(5*n + 1/2) / (3*sqrt(Pi*n) * 2^(8*n - 1/2)). - Vaclav Kotesovec, Apr 05 2024
a(n) = Sum_{k=0..floor(n/2)} binomial(5*n+1,n-2*k). - Seiichi Manyama, Apr 09 2024
a(n) = binomial(1+5*n, n)*hypergeom([1, (1-n)/2, -n/2], [1+2*n, 3/2+2*n], 1). - Stefano Spezia, Apr 09 2024
MATHEMATICA
Table[32^n - Binomial[5*n, 1+n] * Hypergeometric2F1[1, 1 - 4*n, 2+n, -1], {n, 0, 20}] (* Vaclav Kotesovec, Apr 05 2024 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(5*n, k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 05 2024
STATUS
approved