A176753 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)=1, k=0 and l=-2.
1, 1, 0, -1, -4, -12, -34, -93, -248, -644, -1622, -3932, -9054, -19314, -36066, -48953, 8372, 415848, 2180870, 8609676, 29858358, 95443242, 286747530, 815867808, 2199049782, 5577559986, 13083598882, 27240793594, 44583397354
Offset: 0
Examples
a(2)=2*1*1-2=0. a(3)=1-2=-1. a(4)=2*1*(-1)-2=-4.
Crossrefs
Cf. A176752.
Programs
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Maple
l:=-2: : k := 0 : m:=1: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);
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*(1-3*n)*a(n-1) +(9*n-13)*a(n-2) +2*(2*n-9)*a(n-3) +8*(4-n)*a(n-4)=0. - R. J. Mathar, Jul 24 2012