A325216 G.f. A(x) satisfies: 1 = Sum_{n>=0} (1 + 3*x)^(n^3) / A(x)^(n^2) * 1/2^(n+1).

1, 13, 2169, 2978509, 9280313659, 48235745422023, 369813382363308535, 3909740189577825437323, 54527701144836157579584201, 970962668611869711040922366005, 21515265687657935356949478953957425, 580980133435728709625260571749908867477, 18788362634592779032654472355826818388313283, 717059741765903711219719995640847718723285774351

Offset

0,2

Links

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

Example

G.f.: A(x) =1 + 13*x + 2169*x^2 + 2978509*x^3 + 9280313659*x^4 + 48235745422023*x^5 + 369813382363308535*x^6 + 3909740189577825437323*x^7 + ...
such that
1 = 1/2 + (1+3*x)/A(x)*1/2^2 + (1+3*x)^8/A(x)^4*1/2^3 + (1+3*x)^27/A(x)^9*1/2^4 + (1+3*x)^64/A(x)^16*1/2^5 + (1+3*x)^125/A(x)^25*1/2^6 + (1+3*x)^216/A(x)^36*1/2^7 + (1+3*x)^343/A(x)^49*1/2^8 + (1+3*x)^512/A(x)^64*1/2^9 + ...

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, 30*#A+100, (1 + 3*x +x*O(x^#A))^(n^3) / Ser(A)^(n^2) * 1/2^(n+1)*1.), #A-1))/3; ); A[n+1]}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Sequence in context: A283633 A221823 A075601 * A161588 A221927 A013718

Adjacent sequences: A325213 A325214 A325215 * A325217 A325218 A325219

Keyword

nonn

Author

Paul D. Hanna, Apr 19 2019

Status

approved