A325215 - OEIS

%I #6 Apr 20 2019 09:33:24

%S 1,25,60060,1132905020,58664467783190,6255154686240956814,

%T 1192613188256914797257960,371053134042859561147801435880,

%U 176215970882772340084884112291790190,121357690241973072743173180485320899071350,116393177524110499499383856118207410661782097788,150467277168909239442664595062252878406778102486407260,255237617230545143251655215904006414174410609980605014003290

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

%H Paul D. Hanna, <a href="/A325215/b325215.txt">Table of n, a(n) for n = 0..50</a>

%e G.f.: A(x) = 1 + 25*x + 60060*x^2 + 1132905020*x^3 + 58664467783190*x^4 + 6255154686240956814*x^5 + 1192613188256914797257960*x^6 + ...

%e such that

%e 1 = 1/2 + (1+x)/A(x)*1/2^2 + (1+x)^16/A(x)^4*1/2^3 + (1+x)^81/A(x)^9*1/2^4 + (1+x)^256/A(x)^16*1/2^5 + (1+x)^625/A(x)^25*1/2^6 + (1+x)^2401/A(x)^49*1/2^8 + ...

%o (PARI) /* Requires suitable precision */

%o {a(n) = my(A=[1]); for(i=0,n,

%o A=concat(A,0); A[#A] = round( polcoeff( sum(n=0,30*#A+100,(1+x +x*O(x^#A))^(n^4) / Ser(A)^(n^2) * 1/2^(n+1)*1.),#A-1))/3;);A[n+1]}

%o for(n=0,20,print1(a(n),", "))

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 19 2019