A373681 -id:A373681 - 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).

A373683 Expansion of e.g.f. exp(x / (1 - x^2)) / (1 - x^2).

Original entry on oeis.org

1, 1, 3, 13, 61, 441, 3031, 28813, 267513, 3088081, 36278731, 491262861, 6962025973, 108395586313, 1791145742751, 31601369155021, 594291393830641, 11740929829286433, 246910933786777363, 5406641472165854221, 125497950720670828461, 3018786042678264770521

Offset: 0

Seiichi Manyama, Jun 13 2024

nonn

Cf. A373681, A373682.

Cf. A088009.

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

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

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

cp's OEIS Frontend

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

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