A365586 - OEIS

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A365586

Expansion of e.g.f. 1 / (1 + 5 * log(1-x))^(3/5).

1, 3, 27, 390, 7770, 197520, 6108720, 222585360, 9337369920, 443180705520, 23478556469040, 1373311758143520, 87902002849402080, 6111187336982764800, 458573390187299798400, 36939974397639066086400, 3179423992959428231894400, 291190738388834303603395200

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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} (5*j+3)) * |Stirling1(n,k)|.

a(0) = 1; a(n) = Sum_{k=1..n} (5 - 2*k/n) * (k-1)! * binomial(n,k) * a(n-k).

MATHEMATICA

a[n_] := Sum[Product[5*j + 3, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 13 2023 *)

PROG

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+3)*abs(stirling(n, k, 1)));