A202944 G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * 2^(n*(n-1)) * x^n.

1, 3, 24, 640, 61440, 22020096, 30064771072, 158329674399744, 3242591731706757120, 259730156557830486753280, 81704042592835098143342198784, 101249788741429138756344678419791872, 495451126236886402802673428420654515879936

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

The convolution cube-root yields A202943.

Example

 G.f.: A(x) = 1 + 3*x + 24*x^2 + 640*x^3 + 61440*x^4 + 22020096*x^5 +...
where
A(x) = 1 + 3*x + 6*2^2*x^2 + 10*2^6*x^3 + 15*2^12*x^4 + 21*2^20*x^5 +...
Note that the cube root of the g.f. is an integer series:
A(x)^(1/3) = 1 + x + 7*x^2 + 199*x^3 + 20026*x^4 + 7296946*x^5 +...+ A202943(n)*x^n +...

Prog

 (PARI) {a(n)=polcoeff(sum(m=0, n, (m+1)*(m+2)/2*2^(m*(m-1))*x^m+x*O(x^n)), n)}

Crossrefs

Cf. A202943, A202942.

Sequence in context: A318766 A292813 A293249 * A056207 A297561 A326084

Adjacent sequences: A202941 A202942 A202943 * A202945 A202946 A202947

Keyword

nonn

Author

Paul D. Hanna, Dec 26 2011

Status

approved