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

0,18

Links

Table of n, a(n) for n=0..65.

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)).

Prog

(PARI) my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, prod(j=1, 5*k, x^j/(1-x^j))))

Crossrefs

Cf. A000009, A067661, A370747, A372703.

Cf. A363047.

Sequence in context: A033485 A026811 A001401 * A377076 A347549 A008628

Adjacent sequences: A373075 A373076 A373077 * A373079 A373080 A373081

Keyword

nonn

Author

Seiichi Manyama, May 23 2024

Status

approved