|
|
A370704
|
|
a(n) = Sum_{k=0..n} k!*binomial(n, k)*Pochhammer(n, k). Row sums of A370707.
|
|
2
|
|
|
1, 2, 17, 442, 23297, 2029226, 262403857, 47086207442, 11184381577217, 3395509635512242, 1282288601819184401, 589443236677619916362, 324023682525763528809217, 209882061169585594259778842, 158200294157346855067204600337, 137282439597406466709932610293026
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} (-1)^k*Product_{j=0..k-1} (j - n)*(j + n).
a(n) ~ sqrt(Pi) * 4^n * n^(2*n + 1/2) / exp(2*n). - Vaclav Kotesovec, Mar 12 2024
|
|
MAPLE
|
a := n -> local k, j; add((-1)^k * mul((j - n)*(j + n), j = 0..k-1), k = 0..n):
seq(a(n), n = 0..15);
|
|
MATHEMATICA
|
A370704[n_] := Sum[k!*Binomial[n, k]*Pochhammer[n, k], {k, 0, n}];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|