A384810 E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^3)^2 ).

1, 1, 5, 37, 417, 4761, 33313, -1509339, -135791359, -8149132943, -455269648959, -24532196772291, -1260399381304511, -56411711489070807, -1357347436103060191, 146282852689561868821, 35003916010171558562817, 5112183093788001812407521, 647998390863196992450043777

Offset: 0

Author

Seiichi Manyama, Jun 10 2025

Keywords

• sign

Crossrefs

Column k=1 of A384813.

Cf. A052750, A213110, A213111, A384617, A384809.

Programs

PARI

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

Formula

See A384813.