A379870 E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)^3) - x*A(x)^3).

1, 2, 31, 991, 48873, 3276921, 278486359, 28694553119, 3476833863281, 484490228040865, 76339085661865791, 13421203354104200271, 2604724304171427849145, 553128917492225243766065, 127578750880241791377948359, 31761039697155404251033218751, 8488576933611794321694363786849

Offset: 0

Author

Seiichi Manyama, Jan 05 2025

Keywords

• nonn

Crossrefs

Cf. A377890, A379867.

Programs

PARI

a(n) = n!*sum(k=0, n, (4*n-k+1)^(k-1)*binomial(4*n-k+1, n-k)/k!);

Formula

E.g.f.: ( (1/x) * Series_Reversion( x * (exp(-x) - x)^3 ) )^(1/3).

a(n) = n! * Sum_{k=0..n} (4*n-k+1)^(k-1) * binomial(4*n-k+1,n-k)/k!.