A177169 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)=7, k=0 and l=-2.
1, 7, 12, 71, 308, 1752, 9518, 55995, 331024, 2018056, 12445114, 77971468, 493457274, 3154471374, 20324817414, 131901428431, 861253742060, 5654523909972, 37304630338790, 247183333507140, 1644269062695294
Offset: 0
Crossrefs
Cf. A177168.
Programs
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Maple
l:=-2: : k := 0 : m:=7: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) +5*(-3*n+7)*a(n-2) +2*(26*n-81)*a(n-3) +32*(-n+4)*a(n-4)=0. - R. J. Mathar, Jun 14 2016