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A176966 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=1. 1
1, 4, 7, 28, 109, 487, 2233, 10666, 52111, 259957, 1317331, 6765121, 35126623, 184109599, 972775495, 5175914824, 27709135453, 149145574915, 806659265809, 4381711637563, 23893807660885, 130754073218149, 717819706182061 (list; graph; refs; listen; history; text; internal format)
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=1).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +3*(n+1)*a(n-2) +9*(3*n-10)*a(n-3) +36*(-n+4)*a(n-4) +12*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

EXAMPLE

a(2)=2*1*4-2+1=7. a(3)=2*1*7-2+4^2-1+1=28. a(4)=2*1*28-2+2*4*7-2+1=109.

MAPLE

l:=1: : 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. A176964.

Sequence in context: A149078 A149079 A149080 * A117977 A272870 A176750

Adjacent sequences:  A176963 A176964 A176965 * A176967 A176968 A176969

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Apr 29 2010

STATUS

approved

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Last modified January 17 14:57 EST 2020. Contains 330958 sequences. (Running on oeis4.)