|
|
A026773
|
|
a(n) = T(2n-1,n-1), T given by A026769. Also T(2n+1,n+1), T given by A026780.
|
|
11
|
|
|
1, 4, 17, 76, 352, 1674, 8129, 40156, 201236, 1020922, 5234660, 27089726, 141335846, 742712598, 3927908193, 20891799036, 111688381228, 599841215226, 3234957053984, 17512055200470, 95125188934942, 518340392855286, 2832580291316092, 15520177744727766
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2. (End)
a(n) = Sum_{k=0..n} C(n+k+1, n+1)*C(n+1, k)/(k+1).
a(n) = Sum_{k=0..n+1} C(n+2, k)*C(n+k, n+1)/(n+2). (End)
D-finite with recurrence n*(n+1)*a(n) -n*(11*n-7)*a(n-1) +(37*n^2-95*n+54)*a(n-2) +(-49*n^2+269*n-354)*a(n-3) +6*(9*n^2-71*n+138)*a(n-4) -4*(2*n-9)*(n-5)*a(n-5)=0. - R. J. Mathar, Aug 05 2021
|
|
MAPLE
|
seq(coeff(series((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2, x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 01 2019
|
|
MATHEMATICA
|
Rest@CoefficientList[Series[(Sqrt[1-4*x] - Sqrt[1-6*x+x^2])/(2*x) -1/2, {x, 0, 30}], x] (* G. C. Greubel, Nov 01 2019 *)
|
|
PROG
|
(PARI) my(x='x+O('x^30)); Vec((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2) \\ G. C. Greubel, Nov 01 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (Sqrt(1-4*x) - Sqrt(1-6*x+x^2))/(2*x) -1/2 )); // G. C. Greubel, Nov 01 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2).list()
(GAP) List([0..30], n-> Sum([0..n], k-> Binomial(n+1, k)*Binomial(n+k+1, n+1)/(k+1) )); # G. C. Greubel, Nov 01 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|