A116396 Expansion of 2/((2+x)*sqrt(1-4*x)-x).

1, 2, 7, 25, 93, 353, 1358, 5273, 20614, 81003, 319584, 1264924, 5019743, 19963699, 79541181, 317406302, 1268283199, 5073605801, 20316709251, 81427911966, 326612013623, 1310968893954, 5265285993860, 21158914176719, 85071253608611

Offset

0,2

Comments

Diagonal sums of number triangle A116395.

Diagonal sums of the Riordan matrix ((1-sqrt(1-4x))/(2x*sqrt(1-4x)),(1-sqrt(1-4x))/(2*sqrt(1-4x))) (A035324) [Emanuele Munarini, Apr 26 2011]

Links

Table of n, a(n) for n=0..24.

Formula

a(n)=sum{k=0..floor(n/2), (4^(n-k)/2^k)*sum{j=0..k, C(k,j)C(n-k+(j-1)/2,n-k)(-1)^(k-j)}}.

D-finite with recurrence: +2*n*a(n) +(-13*n+10)*a(n-1) +(9*n-16)*a(n-2) +2*(19*n-41)*a(n-3) +(23*n-66)*a(n-4) +2*(2*n-7)*a(n-5)=0. - R. J. Mathar, Jan 24 2020

Mathematica

CoefficientList[Series[(x+(2+x)Sqrt[1-4x])/(2-6x-8x^2-2x^3), {x, 0, 25}], x]) [Emanuele Munarini, Apr 26 2011]

Crossrefs

Sequence in context: A270785 A199247 A242728 * A150453 A150454 A150455

Adjacent sequences: A116393 A116394 A116395 * A116397 A116398 A116399

Keyword

easy,nonn

Author

Paul Barry, Feb 12 2006

Status

approved