A177175 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)=6, k=1 and l=-1.

1, 6, 13, 64, 287, 1515, 8143, 46030, 265909, 1572193, 9443997, 57529101, 354394057, 2204333079, 13823770729, 87311462772, 554904606279, 3546103422655, 22772157825695, 146876986425311, 951065019090195

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) +(2-7*n)*a(n-1) +(19-5*n)*a(n-2) +(43*n-134)*a(n-3) +4*(53-13*n)*a(n-4) +20*(n-5)*a(n-5)=0. - R. J. Mathar, Jul 24 2012

Example

a(2)=2*1*6+2-1=13. a(3)=2*1*13+36+2+1-1=64.

Maple

l:=-1: : k := 1 : m:=6: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. A176832.

Sequence in context: A262238 A111366 A177127 * A301605 A119110 A041305

Adjacent sequences: A177172 A177173 A177174 * A177176 A177177 A177178

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved