A380864 a(n) = [x^n] sqrt(1 - 4*x)/(1 - 8*x). Row sums of A380865.

1, 6, 46, 364, 2902, 23188, 185420, 1483096, 11863910, 94908420, 759257636, 6074027496, 48592102396, 388736403144, 3109889739352, 24879112565936, 199032881137798, 1592262978387044, 12738103567806772, 101904827587176776, 815238617162887828, 6521908924174861784

Offset

0,2

Links

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

Formula

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

D-finite with recurrence: (-48+32*n)*a(n-2) + (6-12*n)*a(n-1) + n*a(n) = 0. - Georg Fischer, Feb 08 2025

Maple

gf := sqrt(1 - 4*x)/(1 - 8*x): ser := series(gf, x, 20): seq(coeff(ser, x, n), n=0..18);

Crossrefs

Cf. A380865.

Sequence in context: A190005 A334609 A253654 * A301421 A288689 A271933

Adjacent sequences: A380861 A380862 A380863 * A380865 A380878 A380879

Keyword

nonn,new

Author

Peter Luschny, Feb 06 2025

Status

approved