A377687 -id:A377687 - cp's OEIS frontend

A377690 E.g.f. satisfies A(x) = 1 + x * (exp(x*A(x)^3) - 1).

1, 0, 2, 3, 76, 545, 11166, 175777, 4012856, 96530625, 2685888730, 83721921041, 2843440273092, 107065956887617, 4332658616388662, 190612061432096865, 8961290146870598896, 451334805268791262337, 24156272027391899229234, 1371678815491898403876913

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A371262, A377687.

a(n) = n!*sum(k=0, n\2, (3*n-3*k)!*stirling(n-k, k, 2)/((n-k)!*(3*n-4*k+1)!));

a(n) = n! * Sum_{k=0..floor(n/2)} (3*n-3*k)! * Stirling2(n-k,k)/( (n-k)! * (3*n-4*k+1)! ).

A377686 E.g.f. satisfies A(x) = (1 - x * log(1 - x*A(x)))^3.

Original entry on oeis.org

1, 0, 6, 9, 312, 2070, 53892, 797580, 21541440, 508313232, 15840608400, 502075577520, 18473543511552, 722232734446080, 31135359390952320, 1435933667363963040, 71392285554374384640, 3782802775152784320000, 213512536856209839796224, 12767785967296083820561920

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A371117, A377685.

Cf. A377391, A377687.

a(n) = 3*n!*sum(k=0, n\2, (3*n-3*k+2)!*abs(stirling(n-k, k, 1))/((n-k)!*(3*n-4*k+3)!));

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377687.

a(n) = 3 * n! * Sum_{k=0..floor(n/2)} (3*n-3*k+2)! * |Stirling1(n-k,k)|/( (n-k)! * (3*n-4*k+3)! ).

cp's OEIS Frontend

A377690 E.g.f. satisfies A(x) = 1 + x * (exp(x*A(x)^3) - 1).

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