A176610 - OEIS

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A176610

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)=0, k=1 and l=1.

1, 0, 3, 10, 25, 65, 197, 652, 2203, 7523, 26159, 92663, 332747, 1206641, 4411883, 16252550, 60270497, 224798517, 842706069, 3173330573, 11998214633, 45531318219, 173359346313, 662062569685, 2535444644053, 9734529981735

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

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=1, l=1).

Conjecture: (n+1)*a(n) +(2-7n)*a(n-1) +(19n-29)*a(n-2) +(110-37n)*a(n-3) +36*(n-4)*a(n-4) +12*(5-n)*a(n-5)=0. - R. J. Mathar, Nov 17 2011

EXAMPLE

a(2)=(1*0+1)+(1*0+1)+1=3. a(3)=2*1*3+2+(0^2+1)+1=10. a(4)=2*1*10+2+2*0*3+2+1=25.

MAPLE

l:=1: : k := 1 : m:=0: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);

CROSSREFS

Sequence in context: A005674 A089100 A089117 * A026965 A130783 A026975

Adjacent sequences: A176607 A176608 A176609 * A176611 A176612 A176613

KEYWORD

nonn

AUTHOR

Richard Choulet, Apr 21 2010

STATUS

approved