A347869 - OEIS

%I #13 May 22 2024 15:12:52

%S 1,2,3,5,7,10,14,21,29,41,55,75,98,131,171,225,290,376,479,613,775,

%T 981,1231,1545,1923,2393,2959,3656,4492,5515,6737,8223,9994,12133,

%U 14676,17732,21351,25679,30793,36879,44049,52549,62535,74329,88153,104418,123437,145746,171765,202193

%N Number of partitions of n such that 5*(greatest part) >= (number of parts).

%C Also, the number of partitions of n such that (greatest part) <= 5*(number of parts).

%F G.f.: Sum_{k>=1} x^k * Product_{j=1..k} (1-x^(5*k+j-1))/(1-x^j).

%o (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*prod(j=1, k, (1-x^(5*k+j-1))/(1-x^j))))

%Y Cf. A064174, A237755, A347867, A347868.

%Y Cf. A348164.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 25 2022