A177200 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)=9, k=-1 and l=1.

1, 9, 17, 113, 529, 3377, 20113, 131761, 859921, 5818417, 39713681, 275857841, 1933976593, 13702864689, 97835776145, 703688999089, 5092141619473, 37053507667505, 270930428700049, 1989695908892593, 14669498823228945

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=-1, l=1).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(-17*n+43)*a(n-2) +3*(29*n-90)*a(n-3) +96*(-n+4)*a(n-4) +32*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*9-2+1=17. a(3)=2*1*17-2+81-1+1=113.

Maple

l:=1: : k := -1 : m:=9: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);

Crossrefs

Cf. A177199.

Sequence in context: A121442 A357567 A049440 * A177166 A073221 A110462

Adjacent sequences: A177197 A177198 A177199 * A177201 A177202 A177203

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved