A361097 E.g.f. A(x) satisfies A(x) = exp( 1/(1 - x/A(x)^3) - 1 ).

1, 1, -3, 22, -251, 3816, -71207, 1542640, -36997431, 929097856, -22062115979, 334968255744, 13395424571725, -2177817789105152, 201597999475333329, -16622491076645341184, 1332634806870147259537, -107073894723559010304000

Offset

0,3

Links

Winston de Greef, Table of n, a(n) for n = 0..359

Formula

a(n) = n! * Sum_{k=0..n} (-3*n+1)^(k-1) * binomial(n-1,n-k)/k!.

E.g.f.: exp( Series_Reversion( x*exp(3*x)/(1+x) ) ). - Seiichi Manyama, Oct 25 2025

a(n) ~ 2 * exp((n-1)/2) * n^(n-1) * sin((sqrt(3)/2 + 2*Pi/3)*n - 1/(2*sqrt(3)) - Pi/4) / 3^(3/4). - Vaclav Kotesovec, Oct 25 2025

Mathematica

Table[n! * Sum[(-3*n+1)^(k-1) * Binomial[n-1, n-k]/k!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 25 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n, (-3*n+1)^(k-1)*binomial(n-1, n-k)/k!);

Crossrefs

Cf. A052873, A361093, A361094, A361095, A361096.

Sequence in context: A136741 A132693 A367845 * A143634 A054595 A054594

Adjacent sequences: A361094 A361095 A361096 * A361098 A361099 A361100

Keyword

sign

Author

Seiichi Manyama, Mar 01 2023

Status

approved