A176854 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)=0, k=-1 and l=0.

1, 0, -2, -7, -18, -37, -52, 10, 412, 1865, 5740, 12922, 16092, -29767, -290264, -1213217, -3608342, -7564363, -6023704, 38816098, 259037300, 991747431, 2756105680, 5061761997, 284694486, -47403203725, -254747436848

Offset

0,3

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=0).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(19*n-29)*a(n-2) +(-17*n+40)*a(n-3) +2*(2*n-7)*a(n-4)=0. - R. J. Mathar, Mar 01 2016

Example

a(2)=2*1*0-2=-2. a(3)=2*1*(-2)-2+0-1=-7. a(4)=2*1*(-7)-2+2*0*(-2)-2=-18.

Maple

l:=0: : k :=-1 : m:=0: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

Sequence in context: A077131 A342397 A212685 * A086741 A229183 A051743

Adjacent sequences: A176851 A176852 A176853 * A176855 A176856 A176857

Keyword

easy,sign

Author

Richard Choulet, Apr 27 2010

Status

approved