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 A261837 Number of compositions of n into distinct parts where each part i is marked with a word of length i over an n-ary alphabet whose letters appear in alphabetical order. 2
 1, 1, 3, 46, 195, 1876, 51114, 322764, 3644355, 43916950, 2427338628, 18277511616, 272107762602, 3507931293608, 62485721142820, 5810222040368296, 53025343448015811, 913540133071336044, 13871534219465464002, 253750203721349071650, 5307815745011707670820 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 FORMULA a(n) = A261835(n,n). MAPLE b:= proc(n, i, p, k) option remember; `if`(i*(i+1)/2n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1)))) end: a:= n-> b(n\$2, 0, n): seq(a(n), n=0..30); MATHEMATICA b[n_, i_, p_, k_] := b[n, i, p, k] = If[i (i + 1)/2 < n, 0, If[n == 0, p!, b[n, i - 1, p, k] + If[i > n, 0, b[n - i, i - 1, p + 1, k]*Binomial[i + k - 1, k - 1]]]]; a[n_] := b[n, n, 0, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jul 12 2021, after Alois P. Heinz *) CROSSREFS Main diagonal of A261835. Sequence in context: A183131 A037105 A196137 * A352756 A059624 A278621 Adjacent sequences: A261834 A261835 A261836 * A261838 A261839 A261840 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 02 2015 STATUS approved

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Last modified March 31 05:21 EDT 2023. Contains 361634 sequences. (Running on oeis4.)