A177167 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=0 and l=-1.

1, 10, 19, 137, 653, 4406, 27077, 185856, 1259601, 8898900, 63225681, 457994141, 3345121235, 24706965674, 183830383235, 1378149812989, 10393740091309, 78828658428280, 600737927801161, 4598286755156991, 35334943369372359

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=0, l=-1).

Conjecture: (n+1)*a(n) +2(1-3n)*a(n-1) +(59-27n)*a(n-2) +4(18n-55)*a(n-3) +40(4-n)*a(n-4)=0. - R. J. Mathar, Nov 27 2011

Example

a(2)=2*1*10-1=19. a(3)=2*1*19+100-1=137.

Maple

l:=-1: : k := 0 : 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

Sequence in context: A253213 A293929 A177203 * A299575 A073222 A110463

Adjacent sequences: A177164 A177165 A177166 * A177168 A177169 A177170

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved