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A176645 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, 11, 42, 177, 817, 3981, 20164, 105027, 558915, 3025287, 16603039, 92169795, 516644985, 2920055107, 16622691454, 95220681081, 548477688005, 3174801937437, 18457766735525, 107734640321681, 631075890235811 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

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) +(11*n-34)*a(n-3) +12*(-n+4)*a(n-4) +4*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 01 2016

EXAMPLE

a(2)=2*1*4+2+1=11. a(3)=2*1*11+2+4^2+1+1=42. a(4)=2*1*42+2+2*4*11+2+1=177.

MAPLE

l:=1: : k := 1 : m:=4: 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

Cf. A176612.

Sequence in context: A149276 A149277 A149278 * A163133 A176574 A323792

Adjacent sequences:  A176642 A176643 A176644 * A176646 A176647 A176648

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Apr 22 2010

STATUS

approved

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Last modified May 11 08:44 EDT 2021. Contains 343784 sequences. (Running on oeis4.)