A377685 -id:A377685 - cp's OEIS frontend

A377682 Expansion of e.g.f. (1 - x * log(1 - x))^2.

1, 0, 4, 6, 40, 180, 948, 5880, 42208, 344736, 3158640, 32091840, 358107264, 4353972480, 57290002560, 811116633600, 12295029657600, 198666240675840, 3408788192947200, 61898371424870400, 1185883197069312000, 23905764186329088000, 505813884019270041600

Offset: 0

Seiichi Manyama, Nov 04 2024

Cf. A377683, A377684.

Cf. A377685.

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

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

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

A377682 Expansion of e.g.f. (1 - x * log(1 - x))^2.

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