A325217 - OEIS

%I #4 Apr 21 2019 07:53:51

%S 1,541,131589873,319256568183829,2893449456351570533383,

%T 70341863181713528175412665891,3789389993653259827703654072650374931,

%U 397173577970161636744184298709009353632613223,73704885033958076138029894062773244745573713507775335,22553355479874698584239261683703801214172076138032015434143979,10765284616745724406271940409799190685067201329824251690320314093963919

%N G.f. A(x) satisfies: 1 = Sum_{n>=0} (1 + 3*x)^(n^5) / A(x)^(n^2) * 1/2^(n+1).

%H Paul D. Hanna, <a href="/A325217/b325217.txt">Table of n, a(n) for n = 0..50</a>

%e G.f.: A(x) = 1 + 541*x + 131589873*x^2 + 319256568183829*x^3 + 2893449456351570533383*x^4 + 70341863181713528175412665891*x^5 + 3789389993653259827703654072650374931*x^6 + ...

%e such that

%e 1 = 1/2 + (1+3*x)/A(x)*1/2^2 + (1+3*x)^32/A(x)^4*1/2^3 + (1+3*x)^243/A(x)^9*1/2^4 + (1+3*x)^1024/A(x)^16*1/2^5 + (1+3*x)^3125/A(x)^25*1/2^6 + (1+3*x)^7776/A(x)^36*1/2^7 + (1+3*x)^16807/A(x)^49*1/2^8 + (1+3*x)^32768/A(x)^64*1/2^9 + (1+3*x)^59049/A(x)^81*1/2^10 + ...

%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, 50*#A+1000, (1 + 3*x +x*O(x^#A))^(n^5) / Ser(A)^(n^2) * 1/2^(n+1)*1.), #A-1))/3; ); A[n+1]}

%o for(n=0, 15, print1(a(n), ", "))

%Y Cf. A325216.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 21 2019