This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A304208 #24 Nov 14 2020 08:37:41 %S A304208 1,1,3,48,1425,66055,4234086,348907094,35277846729,4236771148454, %T A304208 590133028697501,93613602614249377,16671698429605679621, %U A304208 3295006292978246618505,715884159450254458674982,169624990695197593491828744,43538384149387312404895504349 %N A304208 Number of partitions of n^3 into exactly n distinct parts. %H A304208 Alois P. Heinz, <a href="/A304208/b304208.txt">Table of n, a(n) for n = 0..100</a> %F A304208 a(n) = [x^(n^3-n*(n+1)/2)] Product_{k=1..n} 1/(1-x^k). %e A304208 n | Partitions of n^3 into exactly n distinct parts %e A304208 --+------------------------------------------------------------- %e A304208 1 | 1. %e A304208 2 | 7+1 = 6+2 = 5+3. %e A304208 3 | 24+ 2+1 = 23+ 3+1 = 22+ 4+1 = 22+ 3+2 = 21+ 5+1 = 21+ 4+2 %e A304208 | = 20+ 6+1 = 20+ 5+2 = 20+ 4+3 = 19+ 7+1 = 19+ 6+2 = 19+ 5+3 %e A304208 | = 18+ 8+1 = 18+ 7+2 = 18+ 6+3 = 18+ 5+4 = 17+ 9+1 = 17+ 8+2 %e A304208 | = 17+ 7+3 = 17+ 6+4 = 16+10+1 = 16+ 9+2 = 16+ 8+3 = 16+ 7+4 %e A304208 | = 16+ 6+5 = 15+11+1 = 15+10+2 = 15+ 9+3 = 15+ 8+4 = 15+ 7+5 %e A304208 | = 14+12+1 = 14+11+2 = 14+10+3 = 14+ 9+4 = 14+ 8+5 = 14+ 7+6 %e A304208 | = 13+12+2 = 13+11+3 = 13+10+4 = 13+ 9+5 = 13+ 8+6 = 12+11+4 %e A304208 | = 12+10+5 = 12+ 9+6 = 12+ 8+7 = 11+10+6 = 11+ 9+7 = 10+ 9+8. %p A304208 b:= proc(n, i) option remember; `if`(n=0 or i=1, 1, %p A304208 b(n, i-1)+b(n-i, min(i, n-i))) %p A304208 end: %p A304208 a:= n-> b(n^3-n*(n+1)/2, n): %p A304208 seq(a(n), n=0..20); # _Alois P. Heinz_, May 08 2018 %t A304208 $RecursionLimit = 2000; %t A304208 b[n_, i_] := b[n, i] = If[n==0 || i==1, 1, b[n, i-1]+b[n-i, Min[i, n-i]]]; %t A304208 a[n_] := b[n^3 - n(n+1)/2, n]; %t A304208 a /@ Range[0, 20] (* _Jean-François Alcover_, Nov 14 2020, after _Alois P. Heinz_ *) %o A304208 (PARI) {a(n) = polcoeff(prod(k=1, n, 1/(1-x^k+x*O(x^(n^3-n*(n+1)/2)))), n^3-n*(n+1)/2)} %Y A304208 Cf. A107379, A128854, A304176. %K A304208 nonn %O A304208 0,3 %A A304208 _Seiichi Manyama_, May 08 2018