A271622 Expansion of -2/(x*sqrt(4*x+1)+x-2).

1, 1, 2, 2, 5, 2, 18, -19, 115, -296, 1115, -3632, 12868, -44803, 159577, -570455, 2059182, -7476086, 27311129, -100274479, 369888135, -1370063926, 5093782015, -19002596870, 71109902844, -266855928791, 1004045621663, -3786790876945

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = 1 + Sum_{k=1..n-1} (-1)^(n-k-1)*k*binomial(2*n-3*k-1,n-k-1))/(n-k).

a(n) ~ (-1)^n * 2^(2*n+2) / (81*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 11 2016

D-finite with recurrence: (-n+1)*a(n) + 3*(-n+3)*a(n-1) + 2*(2*n-5)*a(n-2) + (n-1)*a(n-3) + 2*(2*n-5)*a(n-4) = 0. - R. J. Mathar, Apr 15 2016

Mathematica

Table[1 + (Sum[(k (-1)^(n - k - 1) Binomial[2 n - 3 k - 1, n - k - 1])/(n - k), {k, 1, n - 1}]), {n, 0, 27}] (* or *)
CoefficientList[Series[-2/(x Sqrt[4 x + 1] + x - 2), {x, 0, 27}], x] (* Michael De Vlieger, Apr 15 2016 *)

Prog

(Maxima)
a(n):=1+(sum(((-1)^(n-k-1)*k*binomial(2*n-3*k-1, n-k-1))/(n-k), k, 1, n-1));
(PARI) x='x+O('x^99); Vec(-2/(x*sqrt(4*x+1)+x-2)) \\ Altug Alkan, Apr 15 2016

Crossrefs

Cf. A000108.

Sequence in context: A114976 A085483 A271654 * A324505 A226135 A284464

Adjacent sequences: A271619 A271620 A271621 * A271623 A271624 A271625

Keyword

sign,easy

Author

Vladimir Kruchinin, Apr 11 2016

Status

approved