A355767 -id:A355767 - cp's OEIS frontend

A356885 E.g.f. satisfies A(x)^(A(x)^2) = 1/(1 - x*A(x))^x.

1, 0, 2, 3, -4, 30, 954, 6300, 6432, 424872, 18273960, 260682840, 1754408424, 47063118960, 2314149100704, 54798086299320, 773632032345600, 20746972036284480, 1072205580591921600, 36098491880448944640, 816375193722964932480, 25160238159364392336000

Offset: 0

Seiichi Manyama, Sep 02 2022

sign

Cf. A184949, A349559, A356786, A356787, A356884.

Cf. A355767.

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

a(n) = n! * Sum_{k=0..floor(n/2)} (n-3*k+1)^(k-1) * |Stirling1(n-k,k)|/(n-k)!.

A355768 E.g.f. satisfies A(x)^(A(x)^2) = 1 + x*A(x).

Original entry on oeis.org

1, 1, -2, 6, -28, 260, -3948, 71120, -1392368, 29971008, -724981920, 19800726528, -603571233120, 20210951379840, -734663902256256, 28785160833254400, -1210241780559067392, 54390280325210271744, -2602745536670709682176, 132118736078618372579328

Offset: 0

Seiichi Manyama, Jul 16 2022

sign

Cf. A000142, A349587.

Cf. A162656, A349650, A355767.

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

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

cp's OEIS Frontend

A356885 E.g.f. satisfies A(x)^(A(x)^2) = 1/(1 - x*A(x))^x.

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