A371927 Expansion of 1/(1 - x/(1 - 8*x^2)^(1/4)).

1, 1, 1, 3, 5, 17, 33, 113, 237, 803, 1769, 5915, 13493, 44547, 104337, 340527, 814397, 2630857, 6399865, 20486905, 50548997, 160507953, 400834465, 1263577141, 3188428301, 9985916077, 25426685961, 79168607025, 203193847381, 629311885861, 1626634117809

Offset: 0

Author

Seiichi Manyama, Jun 07 2024

Keywords

• nonn

Crossrefs

Cf. A373509, A004981.

Programs

Maple

A371927 := proc(n)
    add(8^k*binomial((n+2*k)/4-1,k),k=0..floor(n/2)) ;
end proc:
seq(A371927(n),n=0..70) ; # R. J. Mathar, Jun 07 2024

Mathematica

CoefficientList[Series[1/(1-x/(1-8x^2)^(1/4)),{x,0,30}],x] (* Harvey P. Dale, Dec 20 2024 *)

PARI

a(n) = sum(k=0, n\2, 8^k*binomial((n+2*k)/4-1, k));

Formula

a(n) = Sum_{k=0..floor(n/2)} 8^k * binomial((n+2*k)/4-1,k).