A377438 -id:A377438 - cp's OEIS frontend

A377691 E.g.f. satisfies A(x) = (1 - x * log(1 - x) * A(x))^3.

1, 0, 6, 9, 312, 1530, 47952, 468720, 15273696, 238738752, 8404102080, 185234979600, 7145001364608, 204957002147040, 8705298805015680, 307822476591957600, 14400927608439260160, 604208707715034777600, 31065769175985079142400, 1504405685073556864627200

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A052830, A377438.

Cf. A371141.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371141.

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

A377719 E.g.f. satisfies A(x) = (1 + x * (exp(x) - 1) * A(x))^2.

Original entry on oeis.org

1, 0, 4, 6, 128, 610, 12192, 112154, 2416416, 34337538, 827541200, 16047333082, 436958019984, 10718568174626, 329594991463584, 9737689680629850, 336439401299953472, 11581626068262440194, 446492838289046854320, 17496904148975860376474, 747070411957344952492080

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A371142, A377438.

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

E.g.f.: 4/(1 + sqrt(1 - 4*x*(exp(x) - 1)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371142.
a(n) = 2 * n! * Sum_{k=0..floor(n/2)} (2*k+1)! * Stirling2(n-k,k)/( (n-k)! * (k+2)! ).

cp's OEIS Frontend

A377691 E.g.f. satisfies A(x) = (1 - x * log(1 - x) * A(x))^3.

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