A176280 Diagonal sums of number triangle A046521.

1, 2, 7, 26, 101, 402, 1625, 6638, 27319, 113054, 469811, 1958706, 8187063, 34290934, 143864999, 604402050, 2542083509, 10702020746, 45090876913, 190110250998, 801997354525, 3384971428258, 14292950533517, 60373808435046, 255102065046401, 1078202260326002

Offset

0,2

Comments

Hankel transform is A176281.

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*C(2*(n-k),n-k)/C(2*k,k).

From Vaclav Kotesovec, Oct 21 2012: (Start)

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

Recurrence: n*a(n) = 2*(4*n-3)*a(n-1) - 3*(5*n-8)*a(n-2) - 2*(2*n-3)*a(n-3).

a(n) ~ (2+sqrt(5))^n/(2*sqrt(5)). (End)

Maple

seq(coeff(series(sqrt(1-4*x)/(1-4*x-x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 24 2019

Mathematica

CoefficientList[Series[Sqrt[1-4*x]/(1-4*x-x^2), {x, 0, 30}], x] (* Vaclav Kotesovec, Oct 21 2012 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(sqrt(1-4*x)/(1-4*x-x^2)) \\ G. C. Greubel, Nov 24 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( Sqrt(1-4*x)/(1-4*x-x^2) )); // G. C. Greubel, Nov 24 2019
(Sage)
def A176280_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( sqrt(1-4*x)/(1-4*x-x^2) ).list()
A176280_list(30) # G. C. Greubel, Nov 24 2019

Crossrefs

Sequence in context: A049775 A101850 A279002 * A349713 A045868 A171711

Adjacent sequences: A176277 A176278 A176279 * A176281 A176282 A176283

Keyword

nonn,easy

Author

Paul Barry, Apr 14 2010

Status

approved