A303538 Expansion of ((1 + 8*x)/(1 - 8*x))^(1/8).

1, 2, 2, 44, 86, 1724, 4244, 80024, 223718, 4033132, 12260988, 213418728, 689489148, 11663520216, 39489621864, 652201870896, 2292944058246, 37099981422156, 134565259916012, 2138626858270408, 7964821656989332, 124595233474799752, 474734644904361112

Offset: 0

Author

Seiichi Manyama, Apr 25 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A063886, A303537.

Programs

Maxima

a[n]:=if n<2 then n+1 else (2*a[n-1]+64*(n-2)*a[n-2])/n;
makelist(a[n],n,0,1000); /* Tani Akinari, Apr 29 2018 */

PARI

N=66; x='x+O('x^N); Vec(((1+8*x)/(1-8*x))^(1/8))

Formula

a(n) ~ 2^(3*n + 1/8) / (Gamma(1/8) * n^(7/8)). - Vaclav Kotesovec, Apr 26 2018

n*a(n)-2*a(n-1)-64*(n-2)*a(n-2)=0. - Tani Akinari, Apr 29 2018