A357094 E.g.f. satisfies A(x)^A(x) = (1 - x * A(x))^(log(1 - x * A(x)) / 2).

1, 0, 1, 3, 20, 170, 1789, 22869, 342222, 5874840, 113865786, 2459446440, 58588151148, 1526055579828, 43149414029604, 1316279791377810, 43090904609439900, 1506889769163738432, 56062825134853664328, 2211097753021838716116, 92149286987928381312972

Offset: 0

Author

Seiichi Manyama, Sep 11 2022

Keywords

• nonn

Crossrefs

Cf. A141209, A357095.

Cf. A357036.

Programs

PARI

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

Formula

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

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