A176754 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)=2, k=0 and l=-2.
1, 2, 2, 6, 18, 62, 218, 790, 2914, 10926, 41514, 159558, 619314, 2424414, 9561594, 37956726, 151548930, 608199182, 2452070090, 9926901670, 40338175954, 164471889342, 672683135130, 2759049956566, 11345904429730, 46769328002414
Offset: 0
Examples
a(2)=2*1*2-2=2. a(3)=2*1*2+2^2-2=6. a(4)=2*1*6+2*2*2-2=18.
Crossrefs
Cf. A176653.
Programs
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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);
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*(n-1)*a(n-2) +6*(2*n-7)*a(n-3) +12*(-n+4)*a(n-4)=0. - R. J. Mathar, Feb 18 2016