A177198 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=-1 and l=1.

1, 7, 13, 73, 325, 1837, 10117, 59725, 356293, 2185597, 13583269, 85698973, 546399109, 3518219773, 22835491813, 149279803741, 981896308165, 6493968318781, 43158035158309, 288073454728861, 1930386933091333

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) +(2-7n)*a(n-1) +9*(3-n)*a(n-2) +9*(7n-22)*a(n-3) +72*(4-n)*a(n-4) +24*(n-5)*a(n-5)=0. - R. J. Mathar, Nov 27 2011

Example

a(2)=2*1*7-2+1=13. a(3)=2*1*13-2+49-1+1=73.

Maple

l:=1: : k := -1 : m:=7: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. A177197.

Sequence in context: A219908 A098478 A174878 * A177163 A268350 A061521

Adjacent sequences: A177195 A177196 A177197 * A177199 A177200 A177201

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved