A279136 a(n) = n*Sum_{i=0..n-1} binomial(n,i)*binomial(i-1,n-i-1)/(n-i).

0, 1, 3, 10, 27, 76, 210, 589, 1659, 4708, 13428, 38479, 110682, 319411, 924339, 2681410, 7794939, 22702396, 66229212, 193495279, 566069052, 1658026093, 4861703289, 14269842184, 41922504570, 123265254451, 362719839225, 1068105234304

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: (3*x^3+sqrt(-3*x^2-2*x+1)*(x^2+4*x-3)-3*x^2-7*x+3)/(sqrt(-3*x^2-2*x+1)*(2*x^3-x^2-2*x+1)-3*x^3+x^2+3*x-1).

D-finite with recurrence: +n*a(n) +(-3*n+2)*a(n-1) +2*(-n+1)*a(n-2) +2*(3*n-7)*a(n-3) +(n-2)*a(n-4) +3*(-n+4)*a(n-5)=0. - R. J. Mathar, Mar 12 2017

Prog

(Maxima)
(3*x^3+sqrt(-3*x^2-2*x+1)*(x^2+4*x-3)-3*x^2-7*x+3)/(sqrt(-3*x^2-2*x+1)*(2*x^3-x^2-2*x+1)-3*x^3+x^2+3*x-1);
taylor(%, x, 0, 27);

Crossrefs

Sequence in context: A000501 A154496 A027251 * A127912 A005956 A373279

Adjacent sequences: A279133 A279134 A279135 * A279137 A279138 A279139

Keyword

nonn

Author

Vladimir Kruchinin, Dec 06 2016

Status

approved