login
A115151
Fourth diagonal (M=4) sequence of triangle A113647, called Y(2,1).
1
1, 31, 289, 2271, 16929, 123871, 901153, 6553567, 47759393, 349143007, 2561474593, 18860670943, 139371085857, 1033405464543, 7687240679457, 57356977176543, 429173772386337, 3219806849335263, 24215844242325537
OFFSET
0,2
LINKS
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
Sequence in context: A336279 A156094 A221430 * A327561 A279980 A369173
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 13 2006
STATUS
approved