A268302 G.f.: Sum_{n>=1} x^(n*(n-1)/2) * (G(x)^n + 1/G(x)^(n-1)), where G(x) is the g.f. of A268300.

3, 8, 28, 144, 736, 4024, 22912, 134784, 813476, 5010904, 31379808, 199196320, 1278911808, 8290414024, 54186864896, 356711621984, 2362968349568, 15739688709864, 105357470567228, 708338644347808, 4781146692837856, 32387329985982176, 220104493513881920, 1500273861724289984, 10253983269166864256, 70258772726034956688, 482514972838806347776, 3320848006096569464080, 22900703924095461843008, 158216154716853989543080

Offset: 0

Author

Paul D. Hanna, Feb 26 2016

Keywords

• nonn

Examples

			G.f.: A(x) = 3 + 8*x + 28*x^2 + 144*x^3 + 736*x^4 + 4024*x^5 + 22912*x^6 + 134784*x^7 + 813476*x^8 + 5010904*x^9 + 31379808*x^10 +...
such that
A(x) = Sum_{n>=1} x^(n*(n-1)/2) * (G(x)^n + 1/G(x)^(n-1)),
that is,
A(x) = (G(x) + 1) + x*(G(x)^2 + 1/G(x)) + x^3*(G(x)^3 + 1/G(x)^2) + x^6*(G(x)^4 + 1/G(x)^3) + x^10*(G(x)^5 + 1/G(x)^4) + x^15*(G(x)^6 + 1/G(x)^5) +...,
where
G(x) = 2 + 7*2*x/4 + 119*2*x^2/4^2 + 2118*2*x^3/4^3 + 42523*2*x^4/4^4 + 914922*2*x^5/4^5 + 20745494*2*x^6/4^6 + 487390092*2*x^7/4^7 + 11764545555*2*x^8/4^8 + 289962708802*2*x^9/4^9 +...+ A268300(n)*2*x^n/4^n +...
satisfies:
-1 = Product_{n>=1} (1-x^n) * (1 - x^n/G(x)) * (1 - x^(n-1)*G(x)).
		

Crossrefs

Cf. A268300, A268301.

Formula

G.f.: Product_{n>=1} (1-x^n) * (1 + x^n/G(x)) * (1 + x^(n-1)*G(x)), where G(x) is the g.f. of A268300.