A379824 a(n) = [x^n] 2 / (1 + x*(2*x + 3) + sqrt((x + 1)*(1 - 3*x))). Alternating row sums of A379907.

1, -1, 1, 0, 1, 2, 5, 12, 31, 79, 207, 546, 1457, 3919, 10621, 28968, 79459, 219053, 606611, 1686660, 4706879, 13178956, 37012219, 104235300, 294301801, 832901237, 2362328425, 6713749632, 19116443881, 54526962682, 155785926413, 445772216816, 1277394033603

Offset: 0

Author

Peter Luschny, Jan 06 2025

Keywords

• sign

Crossrefs

Cf. A379907, A114589.

Programs

Maple

a := n -> (-1)^n*add(hypergeom([k-n, k/2+1, (k+1)/2], [1, k + 2], 4), k = 0..n):
seq(simplify(a(n)), n = 0..32);

Formula

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

a(n + 2) + a(n + 3) = A114589(n).