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 A332721 Number of compositions of n^2 with parts <= n, such that each element of [n] is used at least once. 6
 1, 1, 3, 72, 5752, 1501620, 1171326960, 2571831080160, 15245263511750160, 236246829658682027760, 9325247205993698149853760, 917699267902161951609308035200, 221117091698491444413008381486903040, 128433050637127079872089064922773889126400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..50 FORMULA a(n) = A373118(n^2,n). - Alois P. Heinz, May 26 2024 EXAMPLE a(2) = 3: 112, 121, 211. a(3) = 72: 111123, 111132, 111213, 111231, 111312, 111321, 112113, 112131, 112311, 113112, 113121, 113211, 121113, 121131, 121311, 123111, 131112, 131121, 131211, 132111, 211113, 211131, 211311, 213111, 231111, 311112, 311121, 311211, 312111, 321111, 11223, 11232, 11322, 12123, 12132, 12213, 12231, 12312, 12321, 13122, 13212, 13221, 21123, 21132, 21213, 21231, 21312, 21321, 22113, 22131, 22311, 23112, 23121, 23211, 31122, 31212, 31221, 32112, 32121, 32211, 1233, 1323, 1332, 2133, 2313, 2331, 3123, 3132, 3213, 3231, 3312, 3321. MAPLE b:= proc(n, i, p) option remember; `if`(n=0 or i=1, (p+n)! /(n+1)!, add(b(n-i*j, i-1, p+j)/(j+1)!, j=0..n/i)) end: a:= n-> b(n*(n-1)/2, n\$2): seq(a(n), n=0..15); MATHEMATICA b[n_, i_, p_] := b[n, i, p] = If[n == 0 || i == 1, (p + n)!/(n + 1)!, Sum[b[n - i*j, i - 1, p + j]/(j + 1)!, {j, 0, n/i}]]; a[n_] := b[n(n - 1)/2, n, n]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 04 2022, after Alois P. Heinz *) CROSSREFS Cf. A000079, A000290, A103488, A332716, A332747, A332796, A373118. Sequence in context: A322189 A228712 A300967 * A332747 A202948 A213986 Adjacent sequences: A332718 A332719 A332720 * A332722 A332723 A332724 KEYWORD nonn AUTHOR Alois P. Heinz, Feb 21 2020 STATUS approved

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Last modified August 4 01:40 EDT 2024. Contains 374905 sequences. (Running on oeis4.)