|
| |
|
|
A089672
|
|
a(n) = S3(n,4), where S3(n, t) = Sum_{k=0..n} k^t *(Sum_{j=0..k} binomial(n,j))^3.
|
|
4
|
|
|
|
0, 8, 1051, 47024, 1343372, 29595904, 549599246, 9039987264, 135800368320, 1901346478080, 25165027679242, 318105020914208, 3870088369412824, 45584244411107584, 522235732874214800, 5840992473138691072, 63970901725419781632, 687749464543749095424, 7273214936974305201570
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} k^4 *(Sum_{j=0..k} binomial(n,j))^3. - G. C. Greubel, May 26 2022
a(n) ~ 31 * 2^(3*n - 5) * n^5 / 5 * (1 - 15/(62*sqrt(Pi*n)) + (75 - 5*sqrt(3)/Pi) / (31*n)). - Vaclav Kotesovec, May 27 2022
|
|
|
MAPLE
|
S3:= (n, t) -> add(k^t*add(binomial(n, j), j = 0..k)^3, k = 0..n);
seq(S3(n, 4), n = 0..40);
|
|
|
MATHEMATICA
|
a[n_]:= a[n]= Sum[k^4*(Sum[Binomial[n, j], {j, 0, k}])^3, {k, 0, n}];
|
|
|
PROG
|
(SageMath)
def A089672(n): return sum(k^4*(sum(binomial(n, j) for j in (0..k)))^3 for k in (0..n))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
