A298994 Expansion of Product_{n>=1} (1 + (4*x)^n)^(1/2).

1, 2, 6, 52, 134, 956, 4124, 20008, 73158, 439660, 1874612, 8350808, 37583004, 169862616, 779948152, 3774085968, 15435601222, 69542934604, 329825707332, 1403190752632, 6313190864052, 29079505547912, 126937389732872, 552273916408368, 2477249228318748

Offset: 0

Author

Seiichi Manyama, Jan 31 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A271235, A298411, A298993, A303074, A370739.

Programs

Mathematica

CoefficientList[Series[Sqrt[QPochhammer[-1, 4*x]/2], {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 18 2018 *)

Formula

Convolution inverse of A298993.

a(n) ~ 2^(2*n - 2) * exp(Pi*sqrt(n/6)) / (3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 18 2018

Sum_{k=0..n} a(k)*a(n-k) = 4^n * A000009(n). - Vaclav Kotesovec, Jun 07 2025