A365587 - OEIS

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A365587

Expansion of e.g.f. 1 / (1 + 5 * log(1-x))^(4/5).

1, 4, 40, 620, 13020, 345120, 11049960, 414711720, 17851113720, 866838536640, 46873882199520, 2793214943693280, 181854240448514400, 12842833148474299200, 977822088984613771200, 79842750450344086867200, 6959878576257689846265600

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+4)) * |Stirling1(n,k)|.

a(0) = 1; a(n) = Sum_{k=1..n} (5 - k/n) * (k-1)! * binomial(n,k) * a(n-k).

MATHEMATICA

a[n_] := Sum[Product[5*j + 4, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 13 2023 *)

PROG

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+4)*abs(stirling(n, k, 1)));