A358364 a(n) = 16^n * Sum_{k=0..n} binomial(1/2, k)^2.

1, 20, 324, 5200, 83300, 1333584, 21344400, 341580096, 5466017700, 87464462800, 1399525960976, 22393543798080, 358310523944464, 5733141459080000, 91732470946920000, 1467748145667974400, 23484346290765886500, 375754541311565499600, 6012139892071344570000

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = (16*n + 4)*(2*n - 1)^2*a(n - 1) / ((4*n - 3) * n^2).

G.f.: hypergeom([-1/2, -1/2], [1], 16*x)/(1 - 16*x).

a(n) ~ 2^(4*n+2) / Pi. - Vaclav Kotesovec, Nov 14 2023

Maple

a := n -> 16^n*add(binomial(1/2, k)^2, k = 0..n):
seq(a(n), n = 0..18);

Mathematica

a[n_] := 16^n * Sum[Binomial[1/2, k]^2, {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Nov 12 2022 *)

Crossrefs

Cf. A358362, A358363, A358365, A367332.

Sequence in context: A159648 A353106 A078230 * A358541 A304723 A273590

Adjacent sequences: A358361 A358362 A358363 * A358365 A358366 A358367

Keyword

nonn

Author

Peter Luschny, Nov 12 2022

Status

approved