OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Jun Wang and Zhizheng Zhang, On extensions of Calkin's binomial identities, Discrete Math., 274 (2004), 331-342.
FORMULA
a(n) = Sum_{k=0..n} k^3 *(Sum_{j=0..k} binomial(n,j))^3. - G. C. Greubel, May 26 2022
a(n) ~ 15 * 2^(3*n-6) * n^4 * (1 - 2/(5*sqrt(Pi*n)) + (2 - sqrt(3)/(5*Pi))/n). - Vaclav Kotesovec, May 27 2022
MATHEMATICA
a[n_]:= a[n]= Sum[k^3*(Sum[Binomial[n, j], {j, 0, k}])^3, {k, 0, n}];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, May 26 2022 *)
PROG
(SageMath)
def A089671(n): return sum(k^3*(sum(binomial(n, j) for j in (0..k)))^3 for k in (0..n))
[A089671(n) for n in (0..40)] # G. C. Greubel, May 26 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 04 2004
STATUS
approved