A365584 Expansion of e.g.f. 1 / (1 + 4 * log(1-x))^(3/4).

1, 3, 24, 300, 5100, 109692, 2854344, 87164088, 3055516800, 120916282368, 5331444120576, 259168711406976, 13769882994784896, 793844510730348672, 49353915922852214016, 3291455140392403401984, 234388011123877880424960, 17750517946502792294592000

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (4*j+3)) * |Stirling1(n,k)|.

a(0) = 1; a(n) = Sum_{k=1..n} (4 - k/n) * (k-1)! * binomial(n,k) * a(n-k).

a(n) ~ Gamma(1/4) * n^(n + 1/4) / (2^(3/2) * sqrt(Pi) * (exp(1/4) - 1)^(n + 3/4) * exp(3*n/4)). - Vaclav Kotesovec, Nov 11 2023

Mathematica

a[n_] := Sum[Product[4*j + 3, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 10 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 4*j+3)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A347016, A354241, A354264.

Cf. A365567.

Sequence in context: A292186 A365567 A258301 * A138209 A352235 A075142

Adjacent sequences: A365581 A365582 A365583 * A365585 A365586 A365587

Keyword

nonn

Author

Seiichi Manyama, Sep 10 2023

Status

approved