A176953 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, -1, -5, -17, -49, -129, -305, -609, -801, 735, 10911, 53983, 203551, 651487, 1796639, 4084447, 6188831, -4060449, -84814049, -455815457, -1824908513, -6141218081, -17711864033, -42059573537, -67468774625, 33608030943

Offset

0,4

Links

Table of n, a(n) for n=0..26.

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) +(-n-10)*a(n-3) +4*(-4*n+17)*a(n-4) +8*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*1-2-1=-1. a(3)=2*1*(-1)-2+1^2-1-1=-5. a(4)=2*1*(-5)-2+2*1*(-1)-2-1=-17.

Maple

l:=-1: : k := -1 : m:=1: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. A176952.

Sequence in context: A006457 A115981 A083091 * A082753 A000337 A147260

Adjacent sequences: A176950 A176951 A176952 * A176954 A176955 A176956

Keyword

easy,sign

Author

Richard Choulet, Apr 29 2010

Status

approved