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A176858
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)=4, k=-1 and l=0.
1
1, 4, 6, 25, 94, 419, 1884, 8866, 42524, 208361, 1036268, 5222754, 26607772, 136824505, 709211688, 3701711655, 19438809610, 102629612589, 544446273752, 2900686264810, 15514063940500, 83266691903815, 448333365133264
OFFSET
0,2
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=0).
Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +3*(n+1)*a(n-2) +(31*n-104)*a(n-3) +2*(-22*n+89)*a(n-4) +16*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 01 2016
EXAMPLE
a(2)=2*1*4-2=6. a(3)=2*1*6-2+4^2-1=25. a(4)=2*1*25-2+2*4*6-2=94.
MAPLE
l:=0: : k := -1 : m:=4: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. A176857.
Sequence in context: A123055 A272306 A294996 * A182333 A028273 A024471
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Apr 27 2010
STATUS
approved