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%I #7 Sep 20 2020 01:28:19
%S 1,1,2,7,124,14371,12842911,103590035354,8621925847489749,
%T 8307493939404888703058,102488432265617100812550713499,
%U 17706351554929677399562928448484650120,46435685450659378932235460132506329282776942795
%N Number of compositions (ordered partitions) of the n-th n-gonal number into n-gonal numbers.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal 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 * (n - 2) - n + 4) / 2 is the k-th n-gonal number.
%e a(3) = 7 because the third triangular number is 6 and we have [6], [3, 3], [3, 1, 1, 1], [1, 3, 1, 1], [1, 1, 3, 1], [1, 1, 1, 3] and [1, 1, 1, 1, 1, 1].
%Y Cf. A011782, A060354, A224366, A224677, A337762, A337763.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 19 2020
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