A177181 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, 9, 50, 203, 1081, 5491, 30100, 165841, 941019, 5401905, 31489071, 185415573, 1102594901, 6608330597, 39889119774, 242247852507, 1479208979061, 9075878125131, 55927537029301, 345980015040103, 2147862197235447

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) +(-5*n+19)*a(n-2) +(59*n-190)*a(n-3) +4*(-19*n+77)*a(n-4) +28*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*6-2-1=9. a(3)=2*1*9-2+36-1-1=50.

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. A176958.

Sequence in context: A330983 A299914 A187998 * A126110 A372499 A340819

Adjacent sequences: A177178 A177179 A177180 * A177182 A177183 A177184

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved