A363818 -id:A363818 - cp's OEIS frontend

A363816 G.f. satisfies A(x) = (1 + x/A(x))/(1 - x)^2.

1, 3, 2, 8, -9, 62, -230, 1054, -4753, 22208, -105419, 508396, -2482284, 12248430, -60980860, 305955372, -1545397447, 7852100312, -40105277621, 205798130624, -1060467961487, 5485199090834, -28469067353663, 148220323891484, -773892318396664, 4051261817405034

Offset: 0

Seiichi Manyama, Oct 18 2023

sign

Paolo Xausa, Table of n, a(n) for n = 0..1000

Partial sums of A366356.
Cf. A162477, A363818, A364629, A364630.
Cf. A363817, A366363.

A363816[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[2(k-1),n-k]/(2k-1),{k,0,n}];Array[A363816,30,0] (* Paolo Xausa, Oct 20 2023 *)

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

G.f.: A(x) = -2*x / (1-sqrt(1+4*x*(1-x)^2)).

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

A363819 G.f. satisfies A(x) = (1 + x/A(x)^2)/(1 - x)^3.

Original entry on oeis.org

1, 4, 1, 38, -193, 1697, -14298, 127836, -1175835, 11078851, -106354266, 1036575329, -10230191020, 102031153812, -1026763493315, 10412602349343, -106308046392516, 1091783632303656, -11271378486953873, 116907289944782853, -1217649336037820058

Offset: 0

Seiichi Manyama, Oct 18 2023

sign

Cf. A366364, A363818.

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

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

cp's OEIS Frontend

A363816 G.f. satisfies A(x) = (1 + x/A(x))/(1 - x)^2.

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