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A187003 Expansion of 1/(1-x-2*x^2-3*x^3-3*x^4-2*x^5-x^6). 1

%I

%S 1,1,3,8,20,50,126,317,798,2008,5053,12716,32000,80528,202649,509967,

%T 1283334,3229515,8127087,20451846,51467150,129517283,325930746,

%U 820205989,2064051559,5194193770,13071208809,32893747768,82777244097,208309256477,524211053501

%N Expansion of 1/(1-x-2*x^2-3*x^3-3*x^4-2*x^5-x^6).

%H Seiichi Manyama, <a href="/A187003/b187003.txt">Table of n, a(n) for n = 0..2495</a>

%H Kruchinin Vladimir Victorovich, <a href="http://arxiv.org/abs/1009.2565">Composition of ordinary generating functions</a>, arXiv:1009.2565

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,3,3,2,1).

%F a(n):=sum(m=1..n, sum(k=m..n, binomial(m,k-m)*sum(j=0..k, binomial(k,j)*binomial(j,n-3*k+2*j)))), a(0)=1.

%p seq(coeff(series(1/(1-x-2*x^2-3*x^3-3*x^4-2*x^5-x^6),x,n+1), x, n), n = 0 .. 30); # _Muniru A Asiru_, Feb 24 2019

%o (Maxima) a(n):=sum(sum(binomial(m,k-m)*sum(binomial(k,j)*binomial(j,n-3*k+2*j),j,0,k),k,m,n),m,1,n)

%o (PARI) Vec(1/(1-x-2*x^2-3*x^3-3*x^4-2*x^5-x^6)+O(x^44)) \\ _Joerg Arndt_, Mar 04 2011

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, Mar 01 2011

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Last modified August 5 04:03 EDT 2021. Contains 346457 sequences. (Running on oeis4.)