A294436 a(n) = Sum_{m=0..n} (Sum_{k=0..m} binomial(n,k))^5.

1, 33, 1268, 50600, 1972128, 75121312, 2803732096, 102885494016, 3722920064000, 133152625650176, 4715897847097344, 165643005814853632, 5776871664703455232, 200235592430802124800, 6903358709034568712192, 236882142098621090889728, 8094539021386254685569024

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..300

N. J. Calkin, A curious binomial identity, Discr. Math., 131 (1994), 335-337.

M. Hirschhorn, Calkin's binomial identity, Discr. Math., 159 (1996), 273-278.

Formula

a(n) ~ n * 2^(5*n - 1). - Vaclav Kotesovec, Jun 07 2019

Maple

A:=proc(n, k) local j; add(binomial(n, j), j=0..k); end;
S:=proc(n, p) local i; global A; add(A(n, i)^p, i=0..n); end;
[seq(S(n, 5), n=0..30)];

Mathematica

Table[Sum[Sum[Binomial[n, k], {k, 0, m}]^5, {m, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jun 07 2019 *)

Prog

(PARI) a(n) = sum(m=0, n, sum(k=0, m, binomial(n, k))^5); \\ Michel Marcus, Nov 18 2017

Crossrefs

Same expression with exponent b instead of 5: A001792 (b=1), A003583 (b=2), A007403 (b=3), A294435 (b=4).

Sequence in context: A077420 A158688 A353114 * A242492 A065424 A071268

Adjacent sequences: A294433 A294434 A294435 * A294437 A294438 A294439

Keyword

nonn

Author

N. J. A. Sloane, Nov 17 2017

Status

approved