A381905 -id:A381905 - cp's OEIS frontend

A381906 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * B(x)) ), where B(x) is the g.f. of A001764.

1, 3, 15, 100, 787, 6848, 63583, 617350, 6191888, 63650430, 667043379, 7099806346, 76538663840, 833975952491, 9169925032189, 101616966476850, 1133736002540882, 12724529836447420, 143567856744995568, 1627454706916166076, 18526192807286106198, 211694470334287787868

Offset: 0

Seiichi Manyama, Mar 10 2025

nonn

Cf. A381905, A381907.

Cf. A001764, A381881.

a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(2*n+2, n-k)/(n+3*k+1));

G.f. A(x) satisfies A(x) = (1 + x*A(x))^2 * B(x*A(x)).

a(n) = Sum_{k=0..n} binomial(n+3*k+1,k) * binomial(2*n+2,n-k)/(n+3*k+1).

A381907 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * B(x)) ), where B(x) is the g.f. of A001764.

Original entry on oeis.org

1, 4, 25, 197, 1783, 17646, 185622, 2039617, 23149542, 269367631, 3196544816, 38539697456, 470773651286, 5813914938293, 72470441063067, 910587733474165, 11521140613913305, 146659482494039073, 1876975898990490298, 24137070792680577688, 311724732112458291945

Offset: 0

Seiichi Manyama, Mar 10 2025

nonn

Cf. A381905, A381906.

Cf. A001764, A381882.

a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(3*n+3, n-k)/(n+3*k+1));

G.f. A(x) satisfies A(x) = (1 + x*A(x))^3 * B(x*A(x)).

a(n) = Sum_{k=0..n} binomial(n+3*k+1,k) * binomial(3*n+3,n-k)/(n+3*k+1).

cp's OEIS Frontend

A381906 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * B(x)) ), where B(x) is the g.f. of A001764.

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