A357089 -id:A357089 - cp's OEIS frontend

A357088 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2 / 2.

1, 0, 1, 3, 16, 135, 1246, 14238, 192613, 2948025, 51071236, 985911003, 20952667660, 486857940660, 12275673296251, 333786662478363, 9737819506544272, 303399477464036175, 10054949172135522106, 353197317869395005258, 13108298181041284002769

Offset: 0

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349588, A357089.

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

a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n-k+1)^(k-1) * Stirling2(n,2*k)/(2^k * k!).

A357087 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3.

Original entry on oeis.org

1, 0, 0, 6, 36, 150, 2340, 47166, 676116, 10602150, 248197860, 6304530606, 154511054676, 4227889233750, 134462460901860, 4519745455581726, 157756124072317716, 5960350758700381830, 243292987180534250340, 10433760831781705395726, 469420864688765414084436

Offset: 0

Seiichi Manyama, Sep 11 2022

nonn

Cf. A349588, A357086.

Cf. A357085, A357089.

a(n) = sum(k=0, n\3, (3*k)!*(n-k+1)^(k-1)*stirling(n, 3*k, 2)/k!);

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n-k+1)^(k-1) * Stirling2(n,3*k)/k!.

cp's OEIS Frontend

A357088 E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2 / 2.

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