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A176280 Diagonal sums of number triangle A046521. 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A045868 A171711 A129482

Adjacent sequences:  A176277 A176278 A176279 * A176281 A176282 A176283

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Apr 14 2010

STATUS

approved

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)