A337763 - OEIS

%I #9 Sep 19 2020 06:15:02

%S 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,

%T 48,56,62,73,137,126,203,257,256,409,503,612,794,1097,1203,1737,2141,

%U 2773,3322,4527,5087,7497,8214,11238,12598

%N Number of partitions of the n-th n-gonal number into distinct 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/Par#part">Index entries for sequences related to partitions</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%F 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.

%e a(5) = 2 because 5th pentagonal number is 35 and we have [35] and [22, 12, 1].

%Y Cf. A000009, A030273, A060354, A288126, A337762, A337764.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Sep 19 2020