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%I #6 Sep 23 2020 04:19:26
%S 1,1,2,4,13,45,198,858,3728,16115,69125,292940,1224628,5052396,
%T 20570806,82655098,327881398,1284663878,4973614490,19034194696,
%U 72037124003,269723590850,999517370314,3667158097572,13325691939021,47975192145998
%N Number of partitions of the n-th n-gonal pyramidal number into n-gonal pyramidal numbers.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%F 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.
%e 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].
%Y Cf. A006484, A072964, A298269, A337762, A337798, A337799.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 22 2020
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