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A074971 Number of partitions of n into distinct parts of order n. 11
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 6, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 32, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 24, 1, 1, 1, 2, 1, 24, 1, 1, 1, 1, 1, 12, 1, 1, 1, 3, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
Order of partition is lcm of its parts.
LINKS
FORMULA
Coefficient of x^n in expansion of Sum_{i divides n} mu(n/i)*Product_{j divides i} (1+x^j).
EXAMPLE
The a(36) = 6 partitions are (36), (18,12,6), (18,12,4,2), (18,12,3,2,1), (18,9,4,3,2), (12,9,6,4,3,2). - Gus Wiseman, Aug 01 2018
PROG
(PARI) A074971(n) = { my(q=0); fordiv(n, i, my(p=1); fordiv(i, j, p *= (1 + 'x^j)); q += moebius(n/i)*p); polcoeff(q, n); }; \\ Antti Karttunen, Dec 19 2018
CROSSREFS
Cf. also A033630.
Sequence in context: A339790 A334924 A211111 * A344008 A198067 A282749
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Oct 05 2002
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)