A325217 G.f. A(x) satisfies: 1 = Sum_{n>=0} (1 + 3*x)^(n^5) / A(x)^(n^2) * 1/2^(n+1).

1, 541, 131589873, 319256568183829, 2893449456351570533383, 70341863181713528175412665891, 3789389993653259827703654072650374931, 397173577970161636744184298709009353632613223, 73704885033958076138029894062773244745573713507775335, 22553355479874698584239261683703801214172076138032015434143979, 10765284616745724406271940409799190685067201329824251690320314093963919

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..50

Example

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

Prog

(PARI) /* Requires suitable precision */
{a(n) = my(A=[1]); for(i=0, n,
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]}
for(n=0, 15, print1(a(n), ", "))

Crossrefs

Cf. A325216.

Sequence in context: A293582 A331642 A263065 * A232707 A334771 A163764

Adjacent sequences: A325214 A325215 A325216 * A325218 A325219 A325220

Keyword

nonn

Author

Paul D. Hanna, Apr 21 2019

Status

approved