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A249771
Irregular triangle read by rows: T(n,k) is the number of Abelian groups of order A025487(n) with k invariant factors (2 <= n, 1 <= k).
4
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 3, 3, 2, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 4, 3, 2, 1, 1, 1, 5, 2, 2, 1, 3, 1, 3, 3, 2, 1, 1, 1, 1, 3, 5, 1, 2
OFFSET
2,11
COMMENTS
The length of n-th row is A051282(n).
Signatures differing only by a (trailing) list of ones give identical rows.
LINKS
FORMULA
T(n,1) = 1. If k > 1 and the prime signature is (e_1,...,e_s), T(n,k) = Sum(Product(A008284(e_i,k), i in I) * Product(A026820(e_i,k-1), i not in I)), where the sum is taken over nonempty subsets I of {1,...,s}.
T(n,k) = A249770(A025487(n),k).
T(n,1) + T(n,2) = A052304(n).
EXAMPLE
First rows:
1;
1,1;
1;
1,1,1;
1,1;
1,2,1,1;
1,1,1;
1;
1,2,2,1,1;
1,3;
...
CROSSREFS
Refinement of A050360. Last row elements: A249773. Cf. A249770, A052304.
Sequence in context: A037831 A188169 A107039 * A030615 A336766 A375732
KEYWORD
nonn,tabf
AUTHOR
Álvar Ibeas, Nov 06 2014
STATUS
approved