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A337763
Number of partitions of the n-th n-gonal number into distinct n-gonal numbers.
5
1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 4, 4, 2, 2, 4, 7, 8, 5, 6, 14, 6, 13, 23, 16, 19, 32, 34, 48, 56, 62, 73, 137, 126, 203, 257, 256, 409, 503, 612, 794, 1097, 1203, 1737, 2141, 2773, 3322, 4527, 5087, 7497, 8214, 11238, 12598
OFFSET
0,6
FORMULA
a(n) = [x^p(n,n)] Product_{k=1..n} (1 + x^p(n,k)), where p(n,k) = k * (k * (n - 2) - n + 4) / 2 is the k-th n-gonal number.
EXAMPLE
a(5) = 2 because 5th pentagonal number is 35 and we have [35] and [22, 12, 1].
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 19 2020
STATUS
approved