A176678 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=0 and l=-1.

1, 2, 3, 9, 29, 102, 373, 1408, 5441, 21428, 85697, 347133, 1421315, 5872986, 24459731, 102570877, 432725309, 1835333352, 7821313273, 33472882591, 143804772471, 619960227498, 2681200476223, 11629248891246, 50574022963079

Offset

0,2

Links

Table of n, a(n) for n=0..24.

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) +5*(n-1)*a(n-2) +4*(2*n-7)*a(n-3) +8*(-n+4)*a(n-4)=0. - R. J. Mathar, Feb 18 2016

Example

a(2)=2*1*2-1=3. a(3)=2*1*3+2^2-1=9. a(4)=2*1*9+2*2*3-1=29.

Maple

l:=-1: : k := 0 : 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. A176675, A176677.

Sequence in context: A338868 A213943 A153701 * A277251 A275165 A073950

Adjacent sequences: A176675 A176676 A176677 * A176679 A176680 A176681

Keyword

nonn

Author

Richard Choulet, Apr 23 2010

Status

approved