A262720 a(n) = Sum_{k=0..n/2} binomial(n+3,k)*binomial(n+1-k,k+1).

1, 2, 8, 22, 68, 198, 586, 1718, 5047, 14808, 43470, 127636, 374957, 1102078, 3241082, 9537070, 28079357, 82718212, 243809138, 718994032, 2121378272, 6262089436, 18493519148, 54639914652, 161503493023, 477558890378, 1412658185320

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: B'(x)*(1-x/B(x))^2/x^4, where B(x)/x is g.f. of A005043.

Recurrence: n*(n+4)*a(n) = (n^2 + 3*n + 6)*a(n-1) + (n+2)*(5*n + 6)*a(n-2) + 3*(n+1)*(n+2)*a(n-3). - Vaclav Kotesovec, Sep 29 2015

a(n) ~ 3^(n+7/2)/(8*sqrt(Pi*n)). - Vaclav Kotesovec, Sep 29 2015

Mathematica

Table[Sum[Binomial[n+3, k]*Binomial[n+1-k, k+1], {k, 0, n/2}], {n, 0, 25}] (* Vaclav Kotesovec, Sep 29 2015 *)

Prog

(Maxima)
B(x):=(1+x-sqrt(1-2*x-3*x^2))/(2*(1+x));
taylor(diff(B(x), x, 1)*(1-x/B(x))^2/x^4, x, 0, 30);
(PARI) a(n) = sum(k=0, n/2, (binomial(n+3, k)*binomial(n+1-k, k+1))) ;
vector(30, n, a(n-1)) \\ Altug Alkan, Sep 28 2015

Crossrefs

Cf. A005043.

Sequence in context: A137104 A265951 A178159 * A321573 A137103 A089586

Adjacent sequences: A262717 A262718 A262719 * A262721 A262722 A262723

Keyword

nonn

Author

Vladimir Kruchinin, Sep 28 2015

Status

approved