A337763 Number of partitions of the n-th n-gonal number into distinct n-gonal numbers.
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
Keywords
Examples
a(5) = 2 because 5th pentagonal number is 35 and we have [35] and [22, 12, 1].
Links
- Eric Weisstein's World of Mathematics, Polygonal Number
- Index entries for sequences related to partitions
- Index to sequences related to polygonal numbers
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.