A393282 Main diagonal of A330942.

1, 1, 7, 2712, 231522891, 8756434117294432, 249096838614525812698358775, 8139061836900805521792918983553748370384, 433260199304013169377314056431261105381859769023053142147, 50588410365048062214208686025866207883991092439012208028251128999706257554156

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..25

Formula

a(n) ~ exp(n - 1/12) * n^((n-1)*(2*n-1)/2) / (2^(n + 1/2 + log(2)/24) * Pi^(n/2) * log(2)^(n^2 + 1)).

Mathematica

Table[Sum[Binomial[Binomial[j, n]+n-1, n] * Sum[(-1)^(i-j)*Binomial[i, j], {i, j, n^2}], {j, 0, n^2}], {n, 0, 10}]

Prog

(PARI) a(n) = sum(j=0, n^2, binomial(binomial(j, n)+n-1, n)*sum(i=j, n^2, (-1)^(i-j)*binomial(i, j))); \\ Michel Marcus, Feb 08 2026

Crossrefs

Cf. A330942.

Sequence in context: A203705 A354027 A178172 * A234621 A195680 A203587

Adjacent sequences: A393279 A393280 A393281 * A393283 A393284 A393285

Keyword

nonn

Author

Vaclav Kotesovec, Feb 08 2026

Status

approved