A177124 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)=8, k=1 and l=1.

1, 8, 19, 106, 521, 3105, 18581, 117884, 761515, 5044963, 33928351, 231507527, 1597241595, 11128224961, 78169076699, 553043148982, 3937226978193, 28184931742741, 202753591947237, 1464948626336061, 10626428189078521

Offset: 0

Author

Richard Choulet, May 03 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*1*8+2+1=19. a(3)=2*1*19+2+64+1+1=106. a(4)=2*1*106+2+2*8*19+2+1=521.
		

Crossrefs

Cf. A177123.

Programs

Maple

l:=1: : k := 1 : m :=8: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);

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=1, l=1).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(-13*n+35)*a(n-2) +(59*n-178)*a(n-3) +60*(-n+4)*a(n-4) +20*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016