A384855 E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x))^3 ).

1, 1, 7, 10, -503, -8564, -103751, 3479554, 327940225, 8613464536, -36391967279, -24834942253274, -2356662167845487, -88482481533921500, 1825569695231959993, 704791058412273699106, 88829364712362626504449, 5460031123686211024338736, 23871425875449192877470625

Offset: 0

Author

Seiichi Manyama, Jun 10 2025

Keywords

• sign

Crossrefs

Column k=1 of A384859.

Cf. A052752, A213112, A213113, A384856, A384857, A384858.

Cf. A213108, A384617.

Programs

PARI

a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-n+j+k)^(j-1)*binomial(n, j)*a(n-j, 3*j)));

Formula

See A384859.