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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 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A161558 A156094 A221430 * A279980 A001298 A027841

Adjacent sequences:  A115148 A115149 A115150 * A115152 A115153 A115154

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jan 13 2006

STATUS

approved

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Last modified January 17 15:16 EST 2019. Contains 319225 sequences. (Running on oeis4.)