A369808 - 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