A373078 Number of partitions of n into distinct parts such that number of parts is a multiples of 5.
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70, 84, 101, 119, 141, 164, 192, 221, 255, 291, 333, 377, 427, 480, 540, 603, 674, 748, 831, 918, 1014, 1115, 1226, 1342, 1469, 1602, 1748, 1899, 2064, 2236, 2423, 2618, 2829, 3049, 3288, 3537, 3807
Offset: 0
Keywords
Programs
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PARI
my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, prod(j=1, 5*k, x^j/(1-x^j))))
Formula
G.f.: Sum_{k>=0} x^(5*k*(5*k+1)/2) / Product_{j=1..5*k} (1-x^j) = Sum_{k>=0} Product_{j=1..5*k} (x^j/(1-x^j)).