A377691 -id:A377691 - cp's OEIS frontend

A377438 E.g.f. satisfies A(x) = (1 - x * log(1 - x) * A(x))^2.

1, 0, 4, 6, 136, 660, 13668, 128520, 2846240, 41368320, 1021615920, 20260896480, 564541372800, 14159468157120, 445236762450816, 13446791658256320, 474901138629918720, 16708336544212992000, 658279512232521209856, 26360704394322974161920, 1150065728368040063784960

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A052830, A377691.

Cf. A371140.

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

E.g.f.: 4/(1 + sqrt(1 + 4*x*log(1-x)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371140.
a(n) = 2 * n! * Sum_{k=0..floor(n/2)} (2*k+1)! * |Stirling1(n-k,k)|/( (n-k)! * (k+2)! ).

A377720 E.g.f. satisfies A(x) = (1 + x * (exp(x) - 1) * A(x))^3.

Original entry on oeis.org

1, 0, 6, 9, 300, 1455, 44658, 430941, 13821048, 213210171, 7400153550, 160981385433, 6126989357844, 173482562393751, 7273217782923498, 253885773923800245, 11726322434886352368, 485729504795911017075, 24658741688798553168582, 1179026561203600147075857

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A371143, A377691.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371143.

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

cp's OEIS Frontend

A377438 E.g.f. satisfies A(x) = (1 - x * log(1 - x) * A(x))^2.

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