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

Author

Peter Luschny, Feb 06 2025

Keywords

• nonn

Crossrefs

Cf. A380865.

Programs

Maple

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

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