Voozh

A363237

Number of partitions of n with rank a multiple of 5.

1, 0, 1, 1, 1, 3, 3, 4, 6, 8, 12, 15, 21, 27, 34, 47, 59, 77, 98, 125, 160, 200, 251, 315, 390, 488, 602, 744, 913, 1120, 1370, 1669, 2029, 2462, 2975, 3597, 4327, 5203, 6237, 7466, 8919, 10634, 12653, 15035, 17824, 21114, 24950, 29455, 34705, 40844, 47991, 56317, 65987, 77231, 90252

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

LINKS

Table of n, a(n) for n=1..55.

FORMULA

G.f.: (1/Product_{k>=1} (1-x^k)) * Sum_{k>=1} (-1)^(k-1) * x^(k*(3*k-1)/2) * (1-x^k) * (1+x^(5*k)) / (1-x^(5*k)).

MAPLE

b:= proc(n, i, c) option remember; `if`(i>n, 0, `if`(i=n,

`if`(irem(i-c, 5)=0, 1, 0), b(n-i, i, c+1)+b(n, i+1, c)))

end:

a:= n-> b(n, 1$2):