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A337797
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Number of partitions of the n-th n-gonal pyramidal number into n-gonal pyramidal numbers.
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4
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1, 1, 2, 4, 13, 45, 198, 858, 3728, 16115, 69125, 292940, 1224628, 5052396, 20570806, 82655098, 327881398, 1284663878, 4973614490, 19034194696, 72037124003, 269723590850, 999517370314, 3667158097572, 13325691939021, 47975192145998
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..25.
Eric Weisstein's World of Mathematics, Pyramidal Number
Index entries for sequences related to partitions
Index to sequences related to pyramidal numbers
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FORMULA
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a(n) = [x^p(n,n)] Product_{k=1..n} 1 / (1 - x^p(n,k)), where p(n,k) = k * (k + 1) * (k * (n - 2) - n + 5) / 6 is the k-th n-gonal pyramidal number.
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EXAMPLE
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a(3) = 4 because the third tetrahedral (or triangular pyramidal) number is 10 and we have [10], [4, 4, 1, 1], [4, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
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CROSSREFS
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Cf. A006484, A072964, A298269, A337762, A337798, A337799.
Sequence in context: A193057 A115600 A007858 * A300931 A286074 A153930
Adjacent sequences: A337794 A337795 A337796 * A337798 A337799 A337800
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Sep 22 2020
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STATUS
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approved
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