A393279 Row 5 of A330942.

1, 1, 842, 5366384, 131163390878, 8756434117294432, 1304290164762650630350, 378961457411383745944574752, 195161403262649528925078012193328, 165812239037868391548576411900518124424, 219813457866728635566612322696950414918390368, 434863272272920412885377243158815771395394283679600

Offset

0,3

Comments

For fixed r > 1, A330942(r,n) ~ c * r^(r*n + 1/2) * n^((r-1)*n) / (2^((r+1)/2) * (r!)^n * exp((r-1)*n) * log(2)^(r*n+1)), where c = 2^(log(2)/4) if r=2 and c = 1 if r>2.

Links

Table of n, a(n) for n=0..11.

Formula

a(n) ~ 5^(4*n + 1/2) * n^(4*n) / (2^(3*n+3) * 3^n * exp(4*n) * log(2)^(5*n+1)).

For n > 0, a(n) = Sum_{j=0..5*n} (binomial(binomial(j,5) + n - 1, n) * Sum_{i=j..5*n} (-1)^(i-j)*binomial(i,j)).

Mathematica

Join[{1}, Table[Sum[Binomial[Binomial[j, 5] + n - 1, n] Sum[(-1)^(i-j) * Binomial[i, j], {i, j, 5*n}], {j, 0, 5*n}], {n, 1, 15}]]

Crossrefs

Cf. A330942.

Sequence in context: A031736 A154473 A093242 * A031527 A252568 A045243

Adjacent sequences: A393276 A393277 A393278 * A393280 A393281 A393282

Keyword

nonn

Author

Vaclav Kotesovec, Feb 08 2026

Status

approved