A176757 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)=5, k=0 and l=-2.
1, 5, 8, 39, 156, 764, 3710, 19075, 99640, 533316, 2895978, 15948420, 88781874, 498980622, 2827021998, 16129973367, 92598274980, 534480546320, 3099969839270, 18057658897612, 105598220332966, 619702140284970
Offset: 0
Examples
a(2)=2*1*5-2=8. a(3)=2*1*8+5^2-2=39. a(4)=2*1*39+2*4*8-2=156.
Crossrefs
Cf. A176756.
Programs
-
Maple
l:=-2: : k := 0 : m:=5: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*(-3*n+1)*a(n-1) +(-7*n+19)*a(n-2) +6*(6*n-19)*a(n-3) +24*(-n+4)*a(n-4)=0. - R. J. Mathar, Feb 18 2016