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A186940 Diagonal sums of number triangle A114709. 2
1, 0, 3, 6, 31, 126, 589, 2772, 13485, 66780, 336207, 1714698, 8841627, 46015002, 241394073, 1275137448, 6776728825, 36208438488, 194388488155, 1048061471886, 5672504958327, 30808982057046, 167864115588325, 917271225518076, 5025659929354981 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

G.f. (for offset 1): (1+3*x-2*x^2-sqrt(1-6*x+x^2))/(2*(3+x-3*x^2+x^3)).

Conjecture: 3*(n+1)*a(n) +(10-17*n)*a(n-1) -6*(n+1)*a(n-2) +10*(2*n-1)*a(n-3) +9*(1-n)*a(n-4) +(n-2)*a(n-5) =0. - R. J. Mathar, Nov 17 2011

a(n) ~ sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^(n+2) / (36 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 01 2014

MATHEMATICA

Rest[CoefficientList[Series[(1+3*x-2*x^2-Sqrt[1-6*x+x^2])/(2*(3+x-3*x^2+x^3)), {x, 0, 20}], x]] (* Vaclav Kotesovec, Feb 01 2014 *)

CROSSREFS

Hankel transform is A186941.

Sequence in context: A154135 A182274 A103091 * A101751 A274999 A133665

Adjacent sequences:  A186937 A186938 A186939 * A186941 A186942 A186943

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 01 2011

EXTENSIONS

More terms from Vincenzo Librandi, Feb 14 2014

STATUS

approved

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Last modified May 18 15:59 EDT 2022. Contains 353816 sequences. (Running on oeis4.)