A132864 Expansion of 1/(1-4x*c(5x)), where c(x) is the g.f. of A000108.

1, 4, 36, 424, 5716, 83544, 1288296, 20637264, 340116276, 5730014584, 98241641656, 1708602483504, 30070563388936, 534554579527024, 9584333758817616, 173120386421418144, 3147337611202622196, 57545643875054919864, 1057492201661230657176

Offset

0,2

Comments

Hankel transform is A135420. - Paul Barry, Sep 15 2009

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*(-1)^k*5^(n-k). - Philippe Deléham, Dec 11 2007

Integral representation: a(n) = (2/Pi)*Integral_{x=0..20} x^n*sqrt(x*(20-x))/(x*(16+x)). - Paul Barry, Sep 15 2009

From Gary W. Adamson, Jul 18 2011: (Start)

a(n) = upper left term in M^n, M = an infinite square production matrix as follows:

4, 4, 0, 0, 0, 0, ...

5, 5, 5, 0, 0, 0, ...

5, 5, 5, 5, 0, 0, ...

5, 5, 5, 5, 5, 0, ...

5, 5, 5, 5, 5, 5, ...

... (End)

Conjecture: n*a(n) + 2*(15-2*n)*a(n-1) + 160*(3-2*n)*a(n-2) = 0. - R. J. Mathar, Nov 15 2011

a(n) ~ 4^n * 5^(n+1) / (9 * n^(3/2) * sqrt(Pi)). - Vaclav Kotesovec, Feb 08 2014

Mathematica

CoefficientList[Series[1/(1-4*x*(1-Sqrt[1-20*x])/(10*x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 08 2014 *)
Table[5^(n + 1) * CatalanNumber[n] * Hypergeometric2F1[1, n + 1/2, n + 2, -5/4]/4, {n, 0, 18}]  (* Vaclav Kotesovec, Jun 05 2021 *)

Crossrefs

Cf. A000108, A039599, A135420.

Sequence in context: A319175 A317147 A371679 * A294050 A052700 A167540

Adjacent sequences: A132861 A132862 A132863 * A132865 A132866 A132867

Keyword

nonn

Author

Philippe Deléham, Nov 18 2007

Extensions

More terms added by Paul Barry, Sep 15 2009

More terms from Vincenzo Librandi, Feb 11 2014

Status

approved