A292184 a(n) = A291937(3^n).

2, 4, 28, 460, 10774, 80195104, 2894790054826, 122274810705200924689300, 17750307143185064814011639706060016204

Offset: 0

Author

Paul D. Hanna, Oct 05 2017

Keywords

• nonn
• more

Comments

G.f. of A291937 equals: Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^n.

It is surprising that these terms seem to be all positive and increasing so rapidly.

Examples

			These terms are located at positions 3^n of sequence A291937, whose g.f. begins:
G(x) = 1 + (2)*x + (4)*x^3 - 3*x^4 + 6*x^5 - 3*x^6 + 8*x^7 - 15*x^8 + (28)*x^9 - 24*x^10 + 12*x^11 + 14*x^13 - 48*x^14 + 96*x^15 - 95*x^16 + 18*x^17 + 55*x^18 + 20*x^19 - 180*x^20 + 232*x^21 - 120*x^22 + 24*x^23 - 35*x^24 + 76*x^25 - 168*x^26 + (460)*x^27 - 580*x^28 + 30*x^29 + 515*x^30 +...
such that
G(x) = Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^n.
Also,
G(x) = Sum_{n=-oo..+oo} n^2 * x^(2*n) * (1 - x^n)^(n-1).
		

Crossrefs

Cf. A291937.