A381443 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + sinh(x))^3 ).

1, 3, 24, 333, 6720, 179523, 5992800, 240498261, 11287790592, 607019415075, 36813049552896, 2486167829854173, 185070328813031424, 15056826823777670883, 1329283990371617820672, 126573877370649849898149, 12930948581449447912243200, 1410875453109072905123881923

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A377554, A381450.

Cf. A136630, A381430.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(3*n+3, k)*a136630(n, k))/(n+1);

Formula

E.g.f. A(x) satisfies A(x) = (1 + sinh(x*A(x)))^3.

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A381430.

a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(3*n+3,k) * A136630(n,k).