|
%I #3 Mar 15 2013 23:59:21
%S 1,2,-2,4,-8,24,-72,224,-720,2370,-7940,27020,-93128,324424,-1140512,
%T 4041024,-14416030,51737020,-186663414,676656868,-2463300660,
%U 9001715448,-33009329056,121427520528,-447970371792,1657029908094,-6144260440620,22834249359960,-85037438715936
%N G.f.: sqrt( 1 + Sum_{n>=1} 4*x^(n^2) ).
%e G.f.: A(x) = 1 + 2*x - 2*x^2 + 4*x^3 - 8*x^4 + 24*x^5 - 72*x^6 + 224*x^7 - 720*x^8 + 2370*x^9 - 7940*x^10 +...
%e such that
%e A(x)^2 = 1 + 4*x + 4*x^4 + 4*x^9 + 4*x^16 + 4*x^25 + 4*x^36 + 4*x^49 +...+ 4*x^(n^2) +...
%o (PARI) {a(n)=polcoeff(sqrt(1+4*sum(k=1,sqrtint(n)+1,x^(k^2))+x*O(x^n)),n)}
%o for(n=0,20,print1(a(n),", "))
%K sign
%O 0,2
%A _Paul D. Hanna_, Mar 15 2013
|
