A381772 Expansion of ( (1/x) * Series_Reversion( x/((1+x) * C(x))^2 ) )^(1/2), where C(x) is the g.f. of A000108.

1, 2, 11, 83, 727, 6940, 70058, 735502, 7949031, 87851819, 988307647, 11279719247, 130286197186, 1520108988221, 17889102534329, 212095541328931, 2531001870925559, 30376237591559863, 366417240105654587, 4440000077166319993, 54020150448778625847, 659665548217188211288

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * C(x*A(x)^2).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((serreverse(x/((1+x)*(1-sqrt(1-4*x))/(2*x))^2)/x)^(1/2))

Crossrefs

Cf. A054727, A060941, A381773, A381774, A381775.

Cf. A007852, A069271, A381780.

Cf. A000108, A274052.

Sequence in context: A322644 A243408 A352655 * A104086 A143140 A191805

Adjacent sequences: A381769 A381770 A381771 * A381773 A381774 A381775

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2025

Status

approved