A372125 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)*(1 + 4*x*A(x))^(1/2) ).

1, 1, 4, 13, 60, 256, 1252, 5979, 30360, 153626, 801632, 4197284, 22355788, 119695396, 647666544, 3522773337, 19298660772, 106213538104, 587632185580, 3264011196578, 18203515158400, 101862717712340, 571859834176800, 3219573318768300, 18175140989890716

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Index entries for reversions of series

Formula

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

From Seiichi Manyama, Nov 30 2024: (Start)

G.f.: exp( Sum_{k>=1} A378554(k) * x^k/k ).

a(n) = (1/(n+1)) * [x^n] 1/(1 - x*(1 + 4*x)^(1/2))^(n+1).

G.f.: (1/x) * Series_Reversion( x*(1 - x*(1 + 4*x)^(1/2)) ). (End)

Prog

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

Crossrefs

Cf. A001002, A372126.

Cf. A372012, A378554.

Sequence in context: A241470 A219367 A149487 * A320359 A057712 A208592

Adjacent sequences: A372122 A372123 A372124 * A372126 A372127 A372128

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2024

Status

approved