A177166 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=0 and l=-1.

1, 9, 17, 114, 533, 3406, 20281, 132987, 868359, 5880694, 40168271, 279254657, 1959385953, 13894772276, 99289815837, 714761301180, 5176706895201, 37701431645548, 275906664244201, 2028001454003211, 14964925167434231

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(1-3n)*a(n-1) +(51-23n)*a(n-2) +4*(16n-49)*a(n-3) +36*(4-n)*a(n-4)=0. - R. J. Mathar, Nov 27 2011

Example

a(2)=2*1*9-1=17. a(3)=2*1*17+81-1=114.

Maple

l:=-1: : k := 0 : 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. A177165.

Sequence in context: A357567 A049440 A177200 * A073221 A110462 A132375

Adjacent sequences: A177163 A177164 A177165 * A177167 A177168 A177169

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved