A176959 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=1.

1, 0, -1, -4, -11, -25, -47, -62, 7, 421, 1883, 5897, 14599, 27207, 23759, -88160, -611867, -2334109, -6792407, -15438797, -23262579, 6709917, 220802693, 1059222003, 3559089425, 9375216161, 18369306441, 16084068633, -70367438799

Offset

0,4

Links

Table of n, a(n) for n=0..28.

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) +(19*n-29)*a(n-2) +3*(-7*n+18)*a(n-3) +12*(n-4)*a(n-4) +4*(-n+5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*0-2+1=-1. a(3)=2*1*(-1)-2+0-1+1=-4. a(4)=2*1*(-4)-2+2*0*(-1)-2+1=-11.

Maple

l:=1: : 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: A349570 A192597 A181946 * A115294 A110610 A051462

Adjacent sequences: A176956 A176957 A176958 * A176960 A176961 A176962

Keyword

easy,sign

Author

Richard Choulet, Apr 29 2010

Status

approved