A356972 -id:A356972 - cp's OEIS frontend

A356973 E.g.f. satisfies log(A(x)) = (exp(x * A(x)^3) - 1) * A(x).

1, 1, 10, 206, 6555, 283777, 15577332, 1036984027, 81191314678, 7311591070938, 744577308572189, 84608911909469235, 10613728203840498210, 1456899252646375490851, 217215453964895439271178, 34956361099228031471844962, 6039398076840098381458042875

Offset: 0

Seiichi Manyama, Sep 07 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..319

Cf. A052880, A349557, A356972.

Cf. A216136, A356960.

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

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

A356914 E.g.f. satisfies: A(x) = 1/(1 - x * A(x)^2)^A(x).

Original entry on oeis.org

1, 1, 8, 129, 3188, 106820, 4530174, 232744274, 14054237000, 975665799792, 76568358325440, 6703512043934112, 647772783078516600, 68484470168404178928, 7863452609057425825704, 974474039841523412062440, 129636661193226128284609344, 18427094124309886080021680640

Offset: 0

Seiichi Manyama, Sep 07 2022

nonn

Cf. A052813, A349556, A356960.

Cf. A355766, A356972.

m = 18; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x]^2)^A[x] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m-1]! (* Jean-François Alcover, Sep 12 2022 *)

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

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

cp's OEIS Frontend

A356973 E.g.f. satisfies log(A(x)) = (exp(x * A(x)^3) - 1) * A(x).

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