A115151 Fourth diagonal (M=4) sequence of triangle A113647, called Y(2,1).

1, 31, 289, 2271, 16929, 123871, 901153, 6553567, 47759393, 349143007, 2561474593, 18860670943, 139371085857, 1033405464543, 7687240679457, 57356977176543, 429173772386337, 3219806849335263, 24215844242325537

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = A113647(n+3, n+1), n>=0.

G.f.: ((-2 + 8*x +x^3) + 2*(1-6*x+4*x^2)*c(2*x))/((x^3)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).

Recurrence: (n-1)*(n+4)*a(n) = (7*n^2 + 9*n + 8)*a(n-1) + 4*(n+1)*(2*n+1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 5*2^(3*n+9)/(9*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

Mathematica

CoefficientList[Series[((-2+8*x+x^3)+2*(1-6*x+4*x^2)*(1-Sqrt[1-8*x])/(4*x))/((x^3)*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

Crossrefs

Cf. A000108, A113647.

Sequence in context: A336279 A156094 A221430 * A327561 A279980 A369173

Adjacent sequences: A115148 A115149 A115150 * A115152 A115153 A115154

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 13 2006

Status

approved