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A115153 Sixth diagonal (M=6) sequence of triangle A113647, called Y(2,1). 2
1, 127, 1665, 16255, 141441, 1163135, 9273473, 72613759, 562430081, 4327407487, 33161347201, 253517365119, 1935665528961, 14771256557439, 112715410440321, 860346088685439, 6570305359184001, 50209563856600959, 383989436028813441 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n)= A113647(n+5, n+1), n>=0.

G.f.: ((-2 + 16*x - 24*x^2 + x^5) + 2*(1 - 10*x + 24*x^2 - 8*x^3)*c(2*x))/((x^5)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).

Recurrence: (n-1)*(n+6)*a(n) = (7*n^2+23*n+30)*a(n-1) + 4*(n+2)*(2*n+3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 7*2^(3n+13)/(9*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

MATHEMATICA

CoefficientList[Series[((-2+16*x-24*x^2+x^5)+2*(1-10*x+24*x^2-8*x^3)*(1-Sqrt[1-8*x])/(4*x))/((x^5)*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

CROSSREFS

Sequence in context: A258012 A258002 A025598 * A172408 A204216 A075937

Adjacent sequences:  A115150 A115151 A115152 * A115154 A115155 A115156

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jan 13 2006

STATUS

approved

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Last modified May 25 15:54 EDT 2022. Contains 354071 sequences. (Running on oeis4.)