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A176957 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, 5, 22, 79, 353, 1551, 7192, 33789, 162387, 791013, 3905115, 19480249, 98078377, 497676217, 2542770602, 13070074447, 67540608437, 350682097767, 1828571411257, 9571449473587, 50275314445747, 264915701312467 (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) +(35*n-118)*a(n-3) +4*(-13*n+53)*a(n-4) +20*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

EXAMPLE

a(2)=2*1*4-2-1=5. a(3)=2*1*5-2+4^4-1-1=22. a(4)=2*1*22-2+2*4*5-2-1=79.

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. A176956.

Sequence in context: A141447 A129346 A291670 * A341586 A010302 A338422

Adjacent sequences:  A176954 A176955 A176956 * A176958 A176959 A176960

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Apr 29 2010

STATUS

approved

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Last modified March 5 16:55 EST 2021. Contains 341827 sequences. (Running on oeis4.)