A378410 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,k-1) * binomial(n*k,k) / ((n-1)*k+1).

1, 1, 1, 7, 85, 1581, 40006, 1288729, 50578445, 2344950745, 125538581926, 7626452229331, 518557071012696, 39027861427630167, 3221686807607369921, 289464281567009809303, 28124498248184961490621, 2938498159807193630239281, 328556126358414341918608978

Offset

0,4

Links

Table of n, a(n) for n=0..18.

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

Crossrefs

Cf. A349364, A378326, A378327, A378409.

Sequence in context: A056547 A293055 A363357 * A121020 A060237 A000424

Adjacent sequences: A378407 A378408 A378409 * A378411 A378412 A378413

Keyword

nonn

Author

Vaclav Kotesovec, Nov 25 2024

Status

approved