A176752 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=0 and l=-2.

1, 0, -2, -6, -14, -26, -30, 30, 330, 1286, 3538, 6910, 5434, -28618, -182302, -654098, -1693750, -2852570, 264050, 25822302, 126877786, 411465750, 956711938, 1191638734, -2480333334, -23263594746, -96124321390

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=0, l=-2).

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(13*n-21)*a(n-2) +2*(-2*n+3)*a(n-3) +4*(-n+4)*a(n-4)=0. - R. J. Mathar, Feb 18 2016

Example

a(2)=0-2=-2. a(3)=2*1*(-2)-2=-6. a(4)=2*1*(-6)+0-2=-14.

Maple

l:=-2: : k := 0 : m:=2: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: A002703 A230978 A112853 * A140759 A102486 A063620

Adjacent sequences: A176749 A176750 A176751 * A176753 A176754 A176755

Keyword

easy,sign

Author

Richard Choulet, Apr 25 2010

Status

approved