A177185 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)=10, k=-1 and l=-1.

1, 10, 17, 130, 595, 4073, 24459, 167500, 1117353, 7829307, 54906873, 393635415, 2840684509, 20748878557, 152583436237, 1130904562550, 8430522519235, 63205880187653, 476121899816163, 3602456244620557, 27363055273700095

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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*(-7*n+17)*a(n-2) +(107*n-334)*a(n-3) +4*(-31*n+125)*a(n-4) +44*(n-5)*a(n-5)=0. - R. J. Mathar, Feb 21 2016

Example

a(2)=2*1*10-2-1=17. a(3)=2*1*17-2+100-1-1=130.

Maple

l:=-1: : k := -1 : for m from 0 to 10 do 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): od;

Crossrefs

Cf. A177184.

Sequence in context: A058621 A183229 A219879 * A241281 A002744 A320930

Adjacent sequences: A177182 A177183 A177184 * A177186 A177187 A177188

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved