A176958 Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=5, k=-1 and l=-1.

1, 5, 7, 35, 135, 663, 3159, 16055, 82423, 434247, 2317623, 12547975, 68644919, 379136007, 2110601527, 11832031495, 66734423095, 378429810183, 2156265145143, 12339184691207, 70884648719415, 408640406413319

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f f: f(z)=(1-sqrt(1-4*z*(a(0)-z*a(0)^2+z*a(1)+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z) (k=-1, l=-1).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(-n+11)*a(n-2) +(47*n-154)*a(n-3) +4*(-16*n+65)*a(n-4) +24*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*5-2-1=7. a(3)=2*1*7-2+5^2-1-1=35. a(4)=2*1*35-2+2*5*7-2-1=135.

Maple

l:=-1: : k := -1 : m:=5:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);

Crossrefs

Cf. A176957.

Sequence in context: A175667 A341063 A018353 * A196203 A196473 A081851

Adjacent sequences: A176955 A176956 A176957 * A176959 A176960 A176961

Keyword

easy,nonn

Author

Richard Choulet, Apr 29 2010

Status

approved