A384691 E.g.f. A(x) satisfies A(x) = exp( x*A(x) * A(x*A(x))^2 ).

1, 1, 7, 112, 2989, 115136, 5899159, 381657928, 30082660633, 2814548348224, 306467497027531, 38242238970083336, 5401465336487870533, 854848596955885610560, 150317821473136130378335, 29159232358630752927016456, 6201999009581132843649181489, 1438725999127826885623788697472

Offset: 0

Author

Seiichi Manyama, Jun 07 2025

Keywords

• nonn

Crossrefs

Column k=1 of A384692.

Programs

Mathematica

terms = 18; A[] = 0; Do[A[x] = Exp[x*A[x]*A[x*A[x]]^2] + O[x]^terms // Normal, terms]; Range[0,terms-1]!CoefficientList[A[x], x] (* Stefano Spezia, Jun 07 2025 *)

PARI

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

Formula

See A384692.