A368708 a(n) = hypergeom([-1 - n, -n, 1 - n], [2, 3], -2).

1, 1, 3, 13, 69, 417, 2763, 19609, 146793, 1146833, 9278595, 77292261, 659973933, 5756169681, 51137399979, 461691066417, 4228199347281, 39216540096993, 367890444302787, 3486697883136957, 33353178454762389, 321754445379041601, 3127955713554766923, 30624486778208481993, 301790556354721667769, 2991957347531210976817

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = (1/2)*B(n, 2) where B(n, x) are the Baxter polynomials with coefficients A359363, for n > 0. - Peter Luschny, Jan 04 2024

a(n) ~ 3^(n + 7/6) * (2^(2/3) + 2^(1/3) + 1)^(n + 5/3) / (2^(4/3) * Pi * n^4). - Vaclav Kotesovec, Jan 04 2024

Mathematica

Table[HypergeometricPFQ[{-1-n, -n, 1-n}, {2, 3}, -2], {n, 0, 30}] (* Vaclav Kotesovec, Jan 04 2024 *)

Prog

(SageMath)
def A368708(n): return PolyA359363(n, 2) // 2 if n > 0 else 1
print([A368708(n) for n in range(23)])  # Peter Luschny, Jan 04 2024
(Python)
def A368708(n):
    if n == 0: return 1
    return sum(2**k * v for k, v in enumerate(A359363Row(n))) // 2
print([A368708(n) for n in range(26)]) # Peter Luschny, Jan 04 2024

Crossrefs

Cf. A001181, A007724, A217800, A359363, A368709.

Sequence in context: A074534 A153395 A243688 * A352855 A088714 A067145

Adjacent sequences: A368705 A368706 A368707 * A368709 A368710 A368711

Keyword

nonn

Author

Joerg Arndt, Jan 04 2024

Status

approved