A373668 -id:A373668 - cp's OEIS frontend

A373682 Expansion of e.g.f. exp(x / (1 - x^2)^3) / (1 - x^2).

1, 1, 3, 25, 109, 1401, 11191, 147673, 1887705, 26419249, 454408651, 7265533881, 148341346693, 2804459457385, 63733061703039, 1419987630142201, 35144931608633521, 902380834051682913, 24277141650582775315, 699721521711883149529, 20520810981571082937501

Offset: 0

Seiichi Manyama, Jun 13 2024

nonn

Cf. A373681, A373683.

Cf. A373668.

a(n) = n!*sum(k=0, n\2, binomial(3*n-5*k, k)/(n-2*k)!);

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(3*n-5*k,k)/(n-2*k)!.

a(n) == 1 (mod 2).

A373667 Expansion of e.g.f. exp(x / (1 - x^2)^(5/2)).

Original entry on oeis.org

1, 1, 1, 16, 61, 676, 5701, 60376, 798841, 9635536, 160878601, 2367914176, 44902245301, 807083463616, 16799688310861, 358223448539776, 8158048770370801, 199405713714155776, 4987832102850957841, 135848995301247809536, 3737769145322321702701

Offset: 0

Seiichi Manyama, Jun 13 2024

nonn

Cf. A012150, A088009, A373619, A373620, A373668.

a(n) = n!*sum(k=0, n\2, binomial(5*n/2-4*k-1, k)/(n-2*k)!);

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(5*n/2-4*k-1,k)/(n-2*k)!.

a(n) == 1 (mod 15).

cp's OEIS Frontend

A373682 Expansion of e.g.f. exp(x / (1 - x^2)^3) / (1 - x^2).

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