A176611 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)=1, k=1 and l=1.

1, 1, 5, 15, 45, 151, 549, 2083, 8133, 32487, 132141, 545299, 2277021, 9603111, 40844629, 174997363, 754562037, 3271847975, 14257744125, 62407576979, 274256671949, 1209604653095, 5352444701861, 23755193862131

Offset

0,3

Links

Table of n, a(n) for n=0..23.

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) +3*(5*n-7)*a(n-2) +(-25*n+74)*a(n-3) +24*(n-4)*a(n-4) +8*(-n+5)*a(n-5)=0. - R. J. Mathar, Mar 01 2016

Example

a(2)=2*1*1+2+1=5. a(3)=2*1*5+2+1^2+1+1=15. a(4)=2*1*15+2+2*1*5+2+1=45.

Maple

l:=1: : k := 1 : m :=1: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);

Crossrefs

Sequence in context: A099235 A207096 A035069 * A001869 A058425 A079798

Adjacent sequences: A176608 A176609 A176610 * A176612 A176613 A176614

Keyword

easy,nonn

Author

Richard Choulet, Apr 21 2010

Status

approved