A162481 -id:A162481 - cp's OEIS frontend

A381944 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^3, where B(x) is the g.f. of A001764.

1, 4, 16, 89, 655, 5592, 51594, 499159, 4990821, 51140527, 534152690, 5665496618, 60854697427, 660601882734, 7235771990454, 79870211543625, 887569516968685, 9921579561050637, 111487286796322366, 1258604967618419118, 14268057344239960863, 162358119295068686098

Offset: 0

Seiichi Manyama, Mar 10 2025

nonn

Cf. A162481, A366034, A381947.

Cf. A001764.

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

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

A381947 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^3, where B(x) is the g.f. of A002293.

Original entry on oeis.org

1, 4, 17, 111, 1001, 10507, 118986, 1411789, 17307078, 217422098, 2784080234, 36201950786, 476725871599, 6344524132503, 85198695369123, 1152990558752089, 15708685673520617, 215287198676732925, 2965962577091646604, 41052101428818066604, 570583013508324005560

Offset: 0

Seiichi Manyama, Mar 10 2025

nonn

Cf. A162481, A366034, A381944.

Cf. A002293, A381916.

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

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

cp's OEIS Frontend

A381944 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^3, where B(x) is the g.f. of A001764.

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