A177203 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)=10, k=-1 and l=1.

1, 10, 19, 136, 649, 4375, 26893, 184438, 1249507, 8820901, 62634223, 453382597, 3309224059, 24424411627, 181601249779, 1360466777260, 10253089323433, 77706202937131, 591759519723973, 4526303458541383, 34756744887203401

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) +3(17-7n)*a(n-2) +9(11n-34)*a(n-3) +108(4-n)*a(n-4) +36(n-5)*a(n-5)=0. - R. J. Mathar, Nov 27 2011

Example

a(2)=2*1*10-2+1=19. a(3)=2*1*19-2+100-1+1=136.

Maple

l:=1: : k := -1 : for m from 0 to 10 do 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): od;

Crossrefs

Cf. A177200.

Sequence in context: A220005 A253213 A293929 * A177167 A299575 A073222

Adjacent sequences: A177200 A177201 A177202 * A177204 A177205 A177206

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved