A111985 Expansion of g.f.: A(x) = (Sum_{n>=0} (2*n+1)*8^n*x^(n*(n+1)/2))^(1/12).

1, 2, -22, 364, -6490, 124476, -2501116, 51848984, -1099502074, 23722687340, -518856745492, 11473878455400, -256044198076836, 5757405060992728, -130302582530068280, 2965537736183034672, -67820940980720843322, 1557676412999229945932

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..715

Example

G.f.: A(x) = 1 + 2*x - 22*x^2 + 364*x^3 - 6490*x^4 + 124476*x^5 - 2501116*x^6 +...
where
A(x)^12 = 1 + 3*8*x + 5*8^2*x^3 + 7*8^3*x^6 + 9*8^4*x^10 + 11*8^5*x^15 + 13*8^6*x^21 + 15*8^7*x^28 + 17*8^8*x^36 + 19*8^9*x^45 + 21*8^10*x^55 +...

Maple

seq(coeff(series( ( add((2*n+1)*8^n*x^(n*(n+1)/2), n=0..40) )^(1/12), x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 05 2019

Mathematica

CoefficientList[Series[(Sum[(2n+1)*8^n*x^(n(n+1)/2), {n, 0, 40}])^(1/12), {x, 0, 30}], x] (* G. C. Greubel, Nov 05 2019 *)

Prog

(PARI) {a(n)=polcoeff(sum(k=0, sqrtint(2*n+1), (2*k+1)*8^k*x^(k*(k+1)/2)+x*O(x^n))^(1/12), n)}
(Sage) [( (sum((2*n+1)*8^n*x^(n*(n+1)/2) for n in (0..40)) )^(1/12) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Nov 05 2019

Crossrefs

Cf. A111983 (g.f. A(x)^12), A111984 (g.f. A(x)^4).

Sequence in context: A363304 A078232 A151615 * A265860 A138463 A007842

Adjacent sequences: A111982 A111983 A111984 * A111986 A111987 A111988

Keyword

sign

Author

Paul D. Hanna, Aug 25 2005

Status

approved