A371157 Expansion of e.g.f. 1/(1 - x - x^2)^(x^2).

1, 0, 0, 6, 36, 160, 1620, 18648, 220080, 2924640, 44775360, 753207840, 13836731040, 276442882560, 5972081379264, 138607594171200, 3440465206214400, 90951997553464320, 2551374460670538240, 75694365919478960640, 2368107785432883916800

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{j=0..n} Sum_{k=0..floor(j/2)} binomial(j-k,n-j-k) * |Stirling1(j-k,k)|/(j-k)!.

a(n) ~ sqrt(2*Pi) * phi^(n + 1/phi^2) * n^(n + 3/2 - phi)/ (Gamma(1/phi^2) * 5^(1/(2*phi^2)) * exp(n)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Mar 14 2024

Prog

(PARI) a(n) = n!*sum(j=0, n, sum(k=0, j\2, binomial(j-k, n-j-k)*abs(stirling(j-k, k, 1))/(j-k)!));

Crossrefs

Cf. A088369, A371158.

Sequence in context: A263952 A281394 A225380 * A371197 A225012 A228458

Adjacent sequences: A371154 A371155 A371156 * A371158 A371159 A371160

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2024

Status

approved