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A115256
Diagonal sums of correlation triangle of central binomial coefficients.
2
1, 2, 8, 25, 90, 312, 1145, 4186, 15640, 58681, 222298, 845848, 3235385, 12418650, 47827992, 184688185, 714884186, 2772776984, 10774163001, 41932100698, 163430680600, 637793652281, 2491918144602, 9746480252952, 38157725306425
OFFSET
0,2
COMMENTS
Diagonal sums of number triangle A115255.
LINKS
FORMULA
From Vaclav Kotesovec, Mar 02 2014: (Start)
G.f.: 1/(sqrt(1-4x)*sqrt(1-4x^2)*(1-x^3)).
a(n) = Sum_{k=0..floor(n/2)}( Sum_{j=0..n-k} [j<=k]*C(2k-2j, k-j)[j<=n-2k]*C(2n-4k-2j, n-2k-j)}). (End)
a(n) ~ sqrt(3) * 2^(2*n+7) / (189 * sqrt(Pi*n)). - Vaclav Kotesovec, Mar 02 2014
Conjecture: n*a(n) + 2*(-2*n+1)*a(n-1) + 4*(-n+1)*a(n-2) + 3*(5*n-8)*a(n-3) + 2*(2*n-1)*a(n-4) + 4*(n-1)*a(n-5) + 8*(-2*n+3)*a(n-6) = 0. - R. J. Mathar, Jun 22 2016
MATHEMATICA
CoefficientList[Series[1/((Sqrt[1-4x])(Sqrt[1-4x^2])(1-x^3)), {x, 0, 30}], x] (* Harvey P. Dale, Feb 15 2012 *)
PROG
(PARI) x='x+O('x^50); Vec(1/(sqrt(1-4*x)*sqrt(1-4*x^2)*(1-x^3))) \\ G. C. Greubel, Mar 18 2017
CROSSREFS
Sequence in context: A288539 A281338 A036367 * A132963 A122404 A150670
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 18 2006
STATUS
approved