cp's OEIS Frontend

A369809 Expansion of 1/(1 - x^6/(1-x)^7).

%I A369809 #19 Jun 24 2024 05:52:42
%S A369809 1,0,0,0,0,0,1,7,28,84,210,462,925,1730,3108,5565,10388,20944,45697,
%T A369809 104673,242481,553455,1229305,2650221,5565127,11465758,23397041,
%U A369809 47757235,98317135,205108561,433747259,926655972,1989584722,4271185538,9133958765,19421679515
%N A369809 Expansion of 1/(1 - x^6/(1-x)^7).
%C A369809 Number of compositions of 7*n-6 into parts 6 and 7.
%H A369809 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-6,1).
%F A369809 G.f. (1-x)^7/((1-x)^7-x^6).
%F A369809 a(n) = A017847(7*n-6) = Sum_{k=0..floor((7*n-6)/6)} binomial(k,7*n-6-6*k) for n > 0.
%F A369809 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 6*a(n-6) + a(n-7) for n > 7.
%F A369809 a(n) = Sum_{k=0..floor(n/6)} binomial(n-1+k,n-6*k).
%F A369809 a(n) = A373912(n)-A373912(n-1). - _R. J. Mathar_, Jun 24 2024
%o A369809 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^6/(1-x)^7))
%o A369809 (PARI) a(n) = sum(k=0, n\6, binomial(n-1+k, n-6*k));
%Y A369809 Cf. A099253, A369805, A369806, A369807, A369808.
%Y A369809 Cf. A088305, A095263, A290998, A368475, A369794.
%Y A369809 Cf. A000579, A017847.
%K A369809 nonn,easy
%O A369809 0,8
%A A369809 _Seiichi Manyama_, Feb 01 2024