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A261837
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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.
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2
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1, 1, 3, 46, 195, 1876, 51114, 322764, 3644355, 43916950, 2427338628, 18277511616, 272107762602, 3507931293608, 62485721142820, 5810222040368296, 53025343448015811, 913540133071336044, 13871534219465464002, 253750203721349071650, 5307815745011707670820
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history;
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..500
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FORMULA
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a(n) = A261835(n,n).
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MAPLE
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b:= proc(n, i, p, k) option remember;
`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))))
end:
a:= n-> b(n$2, 0, n):
seq(a(n), n=0..30);
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MATHEMATICA
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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 *)
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CROSSREFS
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Main diagonal of A261835.
Sequence in context: A183131 A037105 A196137 * A352756 A059624 A278621
Adjacent sequences: A261834 A261835 A261836 * A261838 A261839 A261840
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Sep 02 2015
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STATUS
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approved
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