Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Feb 02 2024 16:14:59
%S 1,0,0,0,0,1,7,28,84,210,463,938,1821,3563,7385,16577,39529,96315,
%T 232393,546806,1251461,2801015,6189683,13647361,30281870,67918782,
%U 153939843,351309676,803438125,1834160110,4170751775,9443922772,21316094357,48041401423,108291578580
%N Expansion of 1/(1 - x^5/(1-x)^7).
%C Number of compositions of 7*n-5 into parts 5 and 7.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,22,-7,1).
%F a(n) = A369816(7*n-5) for n > 0.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 22*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.
%F a(n) = Sum_{k=0..floor(n/5)} binomial(n-1+2*k,n-5*k).
%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^5/(1-x)^7))
%o (PARI) a(n) = sum(k=0, n\5, binomial(n-1+2*k, n-5*k));
%Y Cf. A099253, A369805, A369806, A369807, A369809.
%Y Cf. A369816.
%K nonn
%O 0,7
%A _Seiichi Manyama_, Feb 01 2024