A177128 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=1.

1, 7, 15, 80, 371, 2088, 11771, 70305, 427405, 2663932, 16853341, 108166507, 701904555, 4599254190, 30383303055, 202154463130, 1353408327935, 9110887281150, 61632613465475, 418751976874065, 2856336340630845

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) +5*(-3*n+7)*a(n-2) +40*(n-3)*a(n-3) +20*(-n+4)*a(n-4)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*7+1=15. a(3)=2*1*15+7^2+1=80.

Maple

l:=1: : k := 0 : m :=7: 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. A177127.

Sequence in context: A042313 A058206 A219523 * A177177 A335758 A343279

Adjacent sequences: A177125 A177126 A177127 * A177129 A177130 A177131

Keyword

easy,nonn

Author

Richard Choulet, May 03 2010

Status

approved