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%I #5 Oct 05 2017 00:18:10
%S 2,4,28,460,10774,80195104,2894790054826,122274810705200924689300,
%T 17750307143185064814011639706060016204
%N a(n) = A291937(3^n).
%C G.f. of A291937 equals: Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^n.
%C It is surprising that these terms seem to be all positive and increasing so rapidly.
%e These terms are located at positions 3^n of sequence A291937, whose g.f. begins:
%e 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 +...
%e such that
%e G(x) = Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^n.
%e Also,
%e G(x) = Sum_{n=-oo..+oo} n^2 * x^(2*n) * (1 - x^n)^(n-1).
%Y Cf. A291937.
%K nonn,more
%O 0,1
%A _Paul D. Hanna_, Oct 05 2017
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