login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Expansion of Product_{n>=1} (1 + (4*x)^n)^(1/2).
10

%I #17 Feb 28 2024 18:10:48

%S 1,2,6,52,134,956,4124,20008,73158,439660,1874612,8350808,37583004,

%T 169862616,779948152,3774085968,15435601222,69542934604,329825707332,

%U 1403190752632,6313190864052,29079505547912,126937389732872,552273916408368,2477249228318748

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

%H Seiichi Manyama, <a href="/A298994/b298994.txt">Table of n, a(n) for n = 0..1000</a>

%F Convolution inverse of A298993.

%F a(n) ~ 2^(2*n - 2) * exp(Pi*sqrt(n/6)) / (3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 18 2018

%t CoefficientList[Series[Sqrt[QPochhammer[-1, 4*x]/2], {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 18 2018 *)

%Y Cf. A298411, A298993, A303074, A370739.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 31 2018