A176755 - OEIS

A176755

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=-2.

1, 3, 4, 15, 52, 208, 846, 3579, 15456, 68096, 304570, 1379980, 6319978, 29211278, 136086710, 638364319, 3012609980, 14293438828, 68139158918, 326218902372, 1567802352910, 7561126873098, 36581288824402, 177496766695528

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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=-2).

Conjecture: (n+1)*a(n) +2*(1-3*n)*a(n-1) +(n+3)*a(n-2) +2*(10*n-33)*a(n-3) +16*(4-n)*a(n-4) =0. - R. J. Mathar, Jul 24 2012

EXAMPLE

a(2)=2*1*3-2=4. a(3)=2*1*4+3^2-2=15. a(4)=2*1*15+2*3*4-2=52.

MAPLE

l:=-2: : 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. A176654.

Sequence in context: A209338 A127144 A042771 * A299684 A211182 A135962

Adjacent sequences: A176752 A176753 A176754 * A176756 A176757 A176758

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Apr 25 2010

STATUS

approved