A378409 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k) / ((n-1)*k+1).

1, 0, 1, 5, 73, 1409, 36601, 1198798, 47594289, 2225255777, 119896198381, 7320401163591, 499766786359501, 37739036987427515, 3123975386959740223, 281348109008473891049, 27391364013973766381281, 2866934827195653717595713, 321048532728871544387444869, 38303867032042004479765603315

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) ~ exp(n - 1/2 - 1/exp(1)) * n^(n - 5/2) / sqrt(2*Pi).

Mathematica

Table[Sum[(-1)^(n-k) * Binomial[n, k] * Binomial[n*k, k]/((n-1)*k + 1), {k, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A346668, A378326, A378327, A378410.

Sequence in context: A222352 A159509 A127167 * A005259 A195636 A213111

Adjacent sequences: A378406 A378407 A378408 * A378410 A378411 A378412

Keyword

nonn

Author

Vaclav Kotesovec, Nov 25 2024

Status

approved