A249519 Expansion of 4*x/(16*x+(sqrt(2)*sqrt(sqrt(1-16*x)+1)-1)*sqrt(1-16*x)-1).

1, 5, 59, 782, 10915, 156890, 2298254, 34115772, 511402275, 7723927970, 117355941274, 1791748546692, 27465854168974, 422452379203652, 6516524753922620, 100771332997219832, 1561717224800526627, 24249283134262469490, 377165907419518984802, 5875218357778513634100

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..830

Formula

G.f.: 4*x/(16*x+(sqrt(2)*sqrt(sqrt(1-16*x)+1)-1)*sqrt(1-16*x)-1).

a(n) = Sum_{i = 0..n} 2^i*binomial(2*n-i-1,n-i)*binomial(2*n+i-1,i).

a(n) ~ (1+sqrt(2)) * 2^(4*n-2) / sqrt(Pi*n). - Vaclav Kotesovec, Oct 31 2014

D-finite with recurrence: n*(2*n-1)*(n-1)*a(n) -2*(n-1)*(32*n^2-64*n+39)*a(n-1) +16*(4*n-5)*(4*n-7)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jun 07 2016

Mathematica

CoefficientList[Series[4 x/(16 x + Sqrt[2] Sqrt[Sqrt[1 - 16 x] + 1] Sqrt[1 - 16 x] - Sqrt[1 - 16 x] - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 31 2014 *)

Prog

(Maxima) a(n):=sum(2^i*binomial(2*n-i-1, n-i)*binomial(2*n+i-1, i), i, 0, n);
(PARI) a(n)=sum(i=0, n, 2^i*binomial(2*n-i-1, n-i)*binomial(2*n+i-1, i)) \\ M. F. Hasler, Oct 31 2014

Crossrefs

Sequence in context: A113055 A020468 A093946 * A371327 A001059 A290702

Adjacent sequences: A249516 A249517 A249518 * A249520 A249521 A249522

Keyword

nonn

Author

Vladimir Kruchinin, Oct 31 2014

Status

approved