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A294436 a(n) = Sum_{m=0..n} (Sum_{k=0..m} binomial(n,k))^5. 5
1, 33, 1268, 50600, 1972128, 75121312, 2803732096, 102885494016, 3722920064000, 133152625650176, 4715897847097344, 165643005814853632, 5776871664703455232, 200235592430802124800, 6903358709034568712192, 236882142098621090889728, 8094539021386254685569024 (list; graph; refs; listen; history; text; internal format)
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.

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)];

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: A262101 A077420 A158688 * A242492 A065424 A071268

Adjacent sequences:  A294433 A294434 A294435 * A294437 A294438 A294439

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 17 2017

STATUS

approved

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Last modified November 14 09:49 EST 2018. Contains 317182 sequences. (Running on oeis4.)