A357036 E.g.f. satisfies A(x) = (1 - x * A(x))^(log(1 - x * A(x)) / 2).

1, 0, 1, 3, 26, 230, 2794, 39564, 663606, 12712104, 275171106, 6632699040, 176309074644, 5123121177096, 161577261004860, 5497133655605760, 200683752698028924, 7825434930630743616, 324616635150708044796, 14273994548639305751040, 663205761925601097418488

Offset: 0

Author

Seiichi Manyama, Sep 09 2022

Keywords

• nonn

Crossrefs

Cf. A001761, A357037.

Cf. A347001, A357028.

Programs

Mathematica

m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = (1 - x*A[x])^(Log[1 - x*A[x]]/2) + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)

PARI

a(n) = sum(k=0, n\2, (2*k)!*(n+1)^(k-1)*abs(stirling(n, 2*k, 1))/(2^k*k!));

Formula

E.g.f. satisfies log(A(x)) = log(1 - x * A(x))^2 / 2.

a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n+1)^(k-1) * |Stirling1(n,2*k)|/(2^k * k!).