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A115152 Fifth diagonal (M=5) sequence of triangle A113647, called Y(2,1). 1
1, 63, 705, 6207, 50113, 389183, 2965441, 22380607, 168132545, 1260716095, 9450356673, 70882689087, 532259536833, 4002476458047, 30145737916353, 227429364793407, 1718693633458113, 13009919057854527, 98641252341252033 (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+4, n+1), n>=0.

G.f.: ((-2 + 12*x - 8*x^2 + x^4) + 2*(1-8*x+12*x^2)*c(2*x))/((x^4)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).

Recurrence: (n-1)*(n+5)*a(n) = (7*n^2+16*n+17)*a(n-1) + 4*(n+1)*(2*n+3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 2^(3*n+12)/(3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

MATHEMATICA

CoefficientList[Series[((-2+12*x-8*x^2+x^4)+2*(1-8*x+12*x^2)*(1-Sqrt[1-8*x])/(4*x))/((x^4)*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

CROSSREFS

Sequence in context: A086578 A198399 A221968 * A284953 A069091 A123866

Adjacent sequences:  A115149 A115150 A115151 * A115153 A115154 A115155

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jan 13 2006

STATUS

approved

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Last modified September 20 20:12 EDT 2019. Contains 327247 sequences. (Running on oeis4.)