A176749 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)=3, k=0 and l=-1.

1, 3, 5, 18, 65, 262, 1093, 4731, 20979, 94930, 436451, 2033321, 9577653, 45538184, 218263593, 1053456780, 5115724797, 24977183908, 122537039845, 603755499411, 2986339566083, 14823218200440, 73813096856015, 368631268757920

Offset

0,2

Links

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

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) +(n+3)*a(n-2) +4*(4*n-13)*a(n-3) +12*(-n+4)*a(n-4)=0. - R. J. Mathar, Feb 18 2016

Example

a(2)=2*1*3-1=5. a(3)=2*1*5+3^2-1=18. a(4)=2*1*18+2*3*5-1=65.

Maple

l:=-1: : k := 0 : m:=3: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. A176678.

Sequence in context: A199676 A303684 A022489 * A145774 A348778 A270894

Adjacent sequences: A176746 A176747 A176748 * A176750 A176751 A176752

Keyword

easy,nonn

Author

Richard Choulet, Apr 25 2010

Status

approved