A367080 - OEIS

A367080

E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2).

1, 1, 5, 50, 766, 15914, 418548, 13337624, 499600848, 21516318360, 1047593782440, 56903921842272, 3411723783002016, 223803339516120480, 15944855840879771232, 1226078375934824887680, 101209861891840507123200, 8926972851724904613537792

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OFFSET

0,3

LINKS

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

FORMULA

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

a(n) ~ (-2 - LambertW(-1, -2*exp(-3)))^(n+1) * (-LambertW(-1, -2*exp(-3)))^n * n^(n-1) / (sqrt(-2 - 2*LambertW(-1, -2*exp(-3))) * exp(n)). - Vaclav Kotesovec, Nov 07 2023

MATHEMATICA

Table[(2*n)! * Sum[Abs[StirlingS1[n, k]]/(2*n-k+1)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 07 2023 *)

PROG

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

CROSSREFS

Cf. A138013, A367152.

Cf. A367078, A367153.

Sequence in context: A047054 A052562 A367136 * A113132 A357333 A088992

Adjacent sequences: A367077 A367078 A367079 * A367081 A367082 A367083

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 07 2023

STATUS

approved