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%I #8 Oct 04 2020 06:12:55
%S 1,1,2,15,2780,94947913,5470124262136760,5979009355803053742719666641,
%T 1610158754567753309521653012201612266212334009,
%U 1566217729562552701894041200097975651072376485590145959656670312797530
%N Number of compositions (ordered 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/Com#comp">Index entries for sequences related to compositions</a>
%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%F a(n) = [x^p(n,n)] 1 / (1 - Sum_{k=1..n} 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) = 15 because the third tetrahedral (or triangular pyramidal) number is 10 and we have [10], [4, 4, 1, 1], [4, 1, 4, 1], [4, 1, 1, 4], [1, 4, 4, 1], [1, 4, 1, 4], [1, 1, 4, 4], [4, 1, 1, 1, 1, 1, 1], [1, 4, 1, 1, 1, 1, 1], [1, 1, 4, 1, 1, 1, 1], [1, 1, 1, 4, 1, 1, 1], [1, 1, 1, 1, 4, 1, 1], [1, 1, 1, 1, 1, 4, 1], [1, 1, 1, 1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
%Y Cf. A006484, A224677, A337764, A337797, A337798.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 22 2020
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