A176855 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=0.

1, 1, 0, -2, -8, -25, -72, -197, -514, -1267, -2884, -5748, -8468, -119, 68688, 382434, 1557232, 5481369, 17494220, 51382510, 138541696, 335629309, 685402744, 919210879, -913800290, -13689355373, -71111254588, -287636394436

Offset

0,4

Links

Table of n, a(n) for n=0..27.

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=0).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +3*(5*n-7)*a(n-2) +(-5*n+4)*a(n-3) +2*(-4*n+17)*a(n-4) +4*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 01 2016

Example

a(2)=2*1*1-2=0. a(3)=2*1*0-2+1-1=-2. a(4)=2*1*(-2)-2+2*1*0-2=-8.

Maple

l:=0: : 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. A176854

Sequence in context: A193048 A301819 A119854 * A309237 A037560 A138804

Adjacent sequences: A176852 A176853 A176854 * A176856 A176857 A176858

Keyword

easy,sign

Author

Richard Choulet, Apr 27 2010

Status

approved