A176952 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, -3, -10, -25, -47, -41, 160, 1093, 3987, 10173, 14835, -20271, -249343, -1106383, -3335310, -6444345, -8187, 67250223, 363173857, 1253557435, 2927919099, 2452549371, -18379498375, -127727251897, -501242196457

Offset

0,3

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=-1, l=-1).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(19*n-29)*a(n-2) +13*(-n+2)*a(n-3) +4*(-n+5)*a(n-4) +4*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 01 2016

Example

a(2)=2*1*0-2-1=-3. a(3)=2*1*(-3)-2+0^2-1-1=-10. a(4)=2*1*(-10)-2+2*0*(-3)-2-1=-25.

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: A340686 A192912 A168062 * A212068 A162607 A267574

Adjacent sequences: A176949 A176950 A176951 * A176953 A176954 A176955

Keyword

easy,sign

Author

Richard Choulet, Apr 29 2010

Status

approved