A372109 G.f. A(x) satisfies A(x) = ( (1 - x*A(x))/(1 - 5*x*A(x)) )^(1/2).

1, 2, 12, 90, 758, 6850, 64904, 636250, 6399120, 65661250, 684665828, 7233956250, 77278356246, 833291781250, 9057750917944, 99144375156250, 1091857567068742, 12089416175781250, 134501879883249300, 1502857085910156250, 16857310306553767026

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for reversions of series

Formula

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

From Seiichi Manyama, Nov 30 2024: (Start)

G.f.: exp( Sum_{k>=1} A378551(k) * x^k/k ).

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

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

Prog

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

Crossrefs

Cf. A001003, A372110.

Cf. A085362, A372018, A372090, A372104, A378551.

Sequence in context: A121357 A098926 A074610 * A250130 A225573 A354233

Adjacent sequences: A372106 A372107 A372108 * A372110 A372111 A372112

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2024

Status

approved