A107233 An inverse Chebyshev transform of n^3.

0, 1, 8, 30, 96, 270, 720, 1820, 4480, 10710, 25200, 58212, 133056, 300300, 672672, 1492920, 3294720, 7220070, 15752880, 34179860, 73902400, 159074916, 341429088, 730122120, 1557593856, 3312591100, 7030805600, 14883258600, 31451414400

Offset: 0

Author

Paul Barry, May 13 2005

Keywords

• easy
• nonn

Comments

Image of n^3 under the mapping of g(x)->(1/sqrt(1-4x^2))g(xc(x^2)) where c(x) is the g.f. of A000108.

Crossrefs

Cf. A000108, A100071, A001787.

Programs

Mathematica

CoefficientList[Series[x*(1 + 4*x) / ((1 - 2*x)^(5/2) * Sqrt[1 + 2*x]), {x, 0, 30}], x] (* Vaclav Kotesovec, Nov 04 2017 *)

Formula

G.f.: 4x(sqrt(1-4x^2)-1)^2(4x+1)/(sqrt(1-4x^2)(sqrt(1-4x^2)+2x-1)^4); a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*(n-2k)^3.

D-finite with recurrence (n-1)*a(n)+4*(n-4)*a(n-1) -4*(n+4)*a(n-2) +16*(2-n)*a(n-3)=0. - R. J. Mathar, Nov 09 2012

From Vaclav Kotesovec, Nov 04 2017: (Start)

G.f.: x*(1 + 4*x) / ((1 - 2*x)^(5/2) * sqrt(1 + 2*x)).

a(n) ~ 2^(n + 1/2) * n^(3/2) / sqrt(Pi). (End)