A177113 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)=2, k=-2 and l=0.

1, 2, 0, -2, -12, -42, -144, -466, -1476, -4522, -13384, -37794, -99964, -237738, -455104, -366706, 2555276, 20416150, 103683976, 445363518, 1736519252, 6310980502, 21595986320, 69654711278, 210206070236, 581729708502

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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=-2, l=0).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(11*n-13)*a(n-2) +15*(n-4)*a(n-3) +2*(-16*n+65)*a(n-4) +12*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*2-4=0. a(3)=2*1*0-4+2^2-2=-2. a(4)=2*1*(-2)-4+2*2*0-4=-12.

Maple

l:=0: : k := -2 : m:=5:d(0):=2: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. A177111.

Sequence in context: A335756 A230813 A367074 * A347010 A281205 A285152

Adjacent sequences: A177110 A177111 A177112 * A177114 A177115 A177116

Keyword

easy,sign

Author

Richard Choulet, May 03 2010

Status

approved