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A102839 a(0)=0, a(1)=1, a(n)=((2*n-1)*a(n-1)+3*n*a(n-2))/(n-1). 0
0, 1, 3, 12, 40, 135, 441, 1428, 4572, 14535, 45925, 144408, 452244, 1411501, 4392675, 13636080, 42237792, 130580451, 403009209, 1241912580, 3821849640, 11746816389, 36064532427, 110610649548, 338928124500, 1037636534025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

n divides a(n) iff the binary representation of n ends with an even number of zeros (i.e. n is in A003159)

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) is asymptotic to c*sqrt(n)*3^n where c=0.2443012(5).....

G.f.: x/(1-2*x-3*x^2)^(3/2). - Vladeta Jovovic, Oct 24 2007

a(n) = 4^(n-1)*JacobiP[n-1,-n-1/2,-n-1/2,-1/2]. - Peter Luschny, May 13 2016

a(n) ~ sqrt(3*n/Pi)*3^n/4. - Vaclav Kotesovec, May 13 2016

MAPLE

seq(add(k*binomial(n, k)*binomial(n-k, k)/2, k=0..n), n=1..26); # Zerinvary Lajos, Oct 23 2007

MATHEMATICA

Table[4^(n-1)*JacobiP[n-1, -n-1/2, -n-1/2, -1/2], {n, 0, 25}] (* Peter Luschny, May 13 2016 *)

PROG

(PARI) a(n)=if(n<2, if(n, 1, 0), 1/(n-1)*((2*n-1)*a(n-1)+3*n*a(n-2)))

CROSSREFS

Sequence in context: A120304 A289652 A026071 * A050182 A222610 A162970

Adjacent sequences:  A102836 A102837 A102838 * A102840 A102841 A102842

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Feb 27 2005

STATUS

approved

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Last modified October 21 14:13 EDT 2018. Contains 316423 sequences. (Running on oeis4.)