A251691 G.f.: G(F(x)) is a power series in x consisting entirely of positive integer coefficients such that G(F(x) - x^k) has negative coefficients for k>0, where G(x) = 1 + x*G(x)^3 is the g.f. of A001764 and F(x) is g.f. of A251690.

1, 1, 2, 4, 8, 17, 36, 78, 169, 370, 813, 1793, 3971, 8817, 19631, 43804, 97938, 219357, 492072, 1105398, 2486320, 5598805, 12620832, 28477139, 64311189, 145354456, 328772330, 744155150, 1685434388, 3819629781, 8661130303, 19649713303, 44601771038, 101285994072, 230110466746

Offset: 0

Author

Paul D. Hanna, Dec 31 2014

Keywords

• nonn

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..120

Crossrefs

Cf. A251690, A001764.

Formula

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 8*x^4 + 17*x^5 + 36*x^6 + 78*x^7 + 169*x^8 + 370*x^9 + 813*x^10 + 1793*x^11 + 3971*x^12 +...

such that A(x) = G(F(x)), where G(x) = 1 + x*G(x)^3 is the g.f. of A001764:

G(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 + 7752*x^7 +...

and F(x) is the g.f. of A251690:

F(x) = x - x^2 - 2*x^3 - 2*x^4 - x^6 - 3*x^8 - 3*x^10 - 3*x^11 - 3*x^13 - 2*x^14 - 3*x^15 - x^16 - 2*x^17 - x^19 - 2*x^20 - 2*x^23 - 2*x^27 - 3*x^29 +...