A268302 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..29.

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.

EXAMPLE

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.

Sequence in context: A355986 A373753 A000239 * A345177 A342139 A195687

Adjacent sequences: A268299 A268300 A268301 * A268303 A268304 A268305

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 26 2016

STATUS

approved