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, 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

Links

Table of n, a(n) for n=0..22.

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

Adjacent sequences: A176855 A176856 A176857 * A176859 A176860 A176861

Keyword

easy,nonn

Author

Richard Choulet, Apr 27 2010

Status

approved