A364764 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 + x*A(x)^4).

1, 1, 1, -2, -14, -27, 70, 625, 1457, -3541, -37403, -98547, 207098, 2564079, 7448923, -12940485, -190014459, -600991549, 827159379, 14802832468, 50584687754, -52159768068, -1193457862093, -4384199208207, 3090291576246, 98618925147291, 388126462227091

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

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

Mathematica

a[n_]:=If[n==0, 1, Sum[(-1)^k*Binomial[n, k]*Binomial[2 n+2*k, n-1-k], {k, 0, n-1}]/n]; Table[a[n], {n, 0, 30}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(2*n+2*k, n-1-k))/n);
(Magma) [1] cat [&+[(-1)^k*Binomial(n, k)*Binomial(2*n+2*k, n-1-k)/n: k in [0..n]] : n in [1..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A291534, A363982, A364051.

Cf. A364739.

Sequence in context: A117705 A330789 A031079 * A355864 A200039 A281206

Adjacent sequences: A364761 A364762 A364763 * A364765 A364766 A364767

Keyword

sign

Author

Seiichi Manyama, Aug 05 2023

Status

approved