A384857 E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^3)^3 ).

1, 1, 7, 46, 361, -6284, -632951, -31583474, -1484748191, -51928436312, -303653774159, 219248741052826, 35743757192135425, 4097960104621191004, 408462300514973323753, 33384541884258873033406, 1521231207001104466842049, -200132739000502301652035888, -84772475888572203988197350303

Offset: 0

Author

Seiichi Manyama, Jun 10 2025

Keywords

• sign

Crossrefs

Column k=1 of A384861.

Cf. A052752, A213112, A213113, A384855, A384856, A384858.

Cf. A213109.

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, 3*j)));

Formula

See A384861.