A162841 - OEIS

%I #6 Nov 09 2019 01:17:55

%S 1,2,30,1988,519862,535771548,2197934140524,36024384044050824,

%T 2361111125528468202534,618965296335059538851784236,

%U 649035869315354547057886734224068,2722257637277195404313634492141394601400,45671920722055969331642704395417211607924522812

%N G.f.: A(x) = sqrt( Sum_{n>=0} 4^(n(n+1)/2)*x^n ).

%H Andrew Howroyd, <a href="/A162841/b162841.txt">Table of n, a(n) for n = 0..50</a>

%e G.f.: A(x) = 1 + 2*x + 30*x^2 + 1988*x^3 + 519862*x^4 +...

%e A(x)^2 = 1 + 4*x + 64*x^2 + 4096*x^3 + 1048576*x^4 +...+ 4^(n(n+1)/2)*x^n +...

%o (PARI) {a(n)=polcoeff(sum(k=0,n,4^(k*(k+1)/2)*x^k +x*O(x^n))^(1/2),n)}

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 14 2009

%E Terms a(11) and beyond from _Andrew Howroyd_, Nov 08 2019