A176828 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)=2, k=1 and l=-1.

1, 2, 5, 16, 55, 203, 791, 3206, 13373, 57009, 247221, 1087029, 4834785, 21712543, 98317921, 448393292, 2057777663, 9495751679, 44033646503, 205087784247, 958968100635, 4500021108229, 21185081246875, 100029600031767

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

G.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) +(11*n-13)*a(n-2) +5*(-n+2)*a(n-3) +4*(-n+5)*a(n-4) +4*(n-5)*a(n-5)=0. - R. J. Mathar, Feb 18 2016

Example

a(2)=2*1*2+2-1=5. a(3)=2*1*5+2+2^2+1-1=16. a(4)=2*1*16+2+2*2*5+2-1=55.

Maple

l:=-1: : k := 1 : m:=2: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. A176826.

Sequence in context: A149970 A157418 A149971 * A149972 A026106 A308027

Adjacent sequences: A176825 A176826 A176827 * A176829 A176830 A176831

Keyword

easy,nonn

Author

Richard Choulet, Apr 27 2010

Status

approved