A371117 - OEIS

A371117

E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)).

1, 0, 2, 3, 32, 210, 2184, 26460, 373344, 6150816, 113958720, 2362345920, 54094694400, 1355708296800, 36926213869440, 1085886303989760, 34291129916574720, 1157362522046277120, 41576054625791078400, 1583864892141097098240, 63779322541075124428800

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OFFSET

0,3

LINKS

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

FORMULA

a(n) = n! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/(n-2*k+1)!.

a(n) ~ sqrt(2 - r*(2*r+1)) * n^(n-1) / (exp(n) * r^n), where r = 0.4599065470184992266076522060382204730855199647380... is the root of the equation 1/r + 2*r*log(r) = 1+r. - Vaclav Kotesovec, Mar 11 2024

MATHEMATICA

nmax = 20; A[_] = 0; Do[A[x_] = 1 - x*Log[1 - x*A[x]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 11 2024 *)

PROG

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

CROSSREFS

Cf. A138013, A371118.

Cf. A371115.

Sequence in context: A357265 A356904 A041895 * A277481 A079883 A358041

Adjacent sequences: A371114 A371115 A371116 * A371118 A371119 A371120

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 11 2024

STATUS

approved