A101602 G.f.: c(3x)^4, c(x) the g.f. of A000108.

1, 12, 126, 1296, 13365, 138996, 1459458, 15466464, 165297834, 1780130520, 19301700924, 210564010080, 2309623985565, 25458117777540, 281857732537050, 3133071216411840, 34953325758094590, 391242268149428520, 4392583646950402020, 49454259823789423200

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: 16/(1+sqrt(1-12x))^4.

a(n)=((8n+12)/(3n+12))((3n+3)/(n+3))3^n*C(n+1).

Conjecture: (n+4)*a(n) - 6*(3*n+7)*a(n-1) + 36*(2*n+1)*a(n-2) = 0. - R. J. Mathar, Nov 15 2011

From Amiram Eldar, May 15 2022: (Start)

Sum_{n>=0} 1/a(n) = 1479/484 - 2691*arcsin(1/(2*sqrt(3)))/(121*sqrt(11)).

Sum_{n>=0} (-1)^n/a(n) = 7569*arcsinh(1/(2*sqrt(3)))/(169*sqrt(13)) - 1767/676. (End)

Mathematica

a[n_] := ((8*n + 12)/(3*n + 12)) * ((3*n + 3)/(n + 3))* 3^n* CatalanNumber[n + 1]; Array[a, 20, 0] (* Amiram Eldar, May 15 2022 *)

Crossrefs

Cf. A000108, A050159, A101600, A101601.

Sequence in context: A159736 A004991 A228008 * A264896 A062199 A199528

Adjacent sequences: A101599 A101600 A101601 * A101603 A101604 A101605

Keyword

easy,nonn

Author

Paul Barry, Dec 08 2004

Status

approved