A177129 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=0 and l=1.

1, 8, 17, 99, 471, 2816, 16535, 103942, 661447, 4327566, 28698915, 193214427, 1314753729, 9035450112, 62597834193, 436806174807, 3066961374135, 21653065678706, 153619938907211, 1094646596551549, 7830810922793173

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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=1).

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-19*n+43)*a(n-2) +48*(n-3)*a(n-3) +24*(-n+4)*a(n-4)=0. - R. J. Mathar, Jun 14 2016

Example

a(2)=2*1*8+1=17. a(3)=2*1*17+64+1=99.

Maple

l:=1: : k := 0 : m :=8: d(0):=1:d(1):=m: for n from 1 to 28 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, 31); seq(d(n), n=0..29);

Crossrefs

Cf. A177128.

Sequence in context: A171065 A134790 A350683 * A177178 A357678 A097405

Adjacent sequences: A177126 A177127 A177128 * A177130 A177131 A177132

Keyword

easy,nonn

Author

Richard Choulet, May 03 2010

Status

approved