A210310 G.f.: [ Sum_{n>=0} (n+1)*(n+2)/2 * 4^(n^2) * x^n ]^(1/3).

1, 4, 496, 869824, 21467623936, 7881126729140224, 44075357435370071351296, 3802951448073847111253622882304, 5104235473390420925196874786915866443776, 107176786696765659714361271737312271270497663320064

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Formula

a(n) == 1 (mod 3).

Example

G.f.: A(x) = 1 + 4*x + 496*x^2 + 869824*x^3 + 21467623936*x^4 +...
where
A(x)^3 = 1 + 3*4*x + 6*4^4*x^2 + 10*4^9*x^3 + 15*4^16*x^4 + 21*4^25*x^5 +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, (m+1)*(m+2)/2*4^(m^2)*x^m+x*O(x^n))^(1/3), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A202942.

Sequence in context: A357536 A330579 A221554 * A324155 A350968 A378310

Adjacent sequences: A210307 A210308 A210309 * A210311 A210312 A210313

Keyword

nonn

Author

Paul D. Hanna, Mar 20 2012

Status

approved