A177130 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, 19, 120, 583, 3688, 22431, 147801, 979425, 6696656, 46323049, 325632187, 2312401207, 16588994570, 119955953891, 873728090530, 6403332744227, 47188541743102, 349446649937015, 2599119078248913, 19407853923218641

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) +(-23*n+51)*a(n-2) +56*(n-3)*a(n-3) +28*(-n+4)*a(n-4)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*9+1=19. a(3)=2*1*19+81+1=120.

Maple

l:=1: : k := 0 : m :=9: 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. A177129.

Sequence in context: A171066 A068174 A165247 * A240120 A177179 A335782

Adjacent sequences: A177127 A177128 A177129 * A177131 A177132 A177133

Keyword

easy,nonn

Author

Richard Choulet, May 03 2010

Status

approved