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URL: https://oeis.org/A327676

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A327676
Total number of colors in all colored compositions of n using all colors of an initial interval of the color palette such that all parts have different color patterns and the patterns for parts i are sorted and have i colors (in arbitrary order).
2
0, 1, 7, 96, 1120, 17133, 318550, 6174409, 134222746, 3227634290, 86758393637, 2455321082763, 75378081090618, 2465367832093301, 85698931156186485, 3188667759545387936, 124641366048950285559, 5131034234304472735967, 222142129822095164108159
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=1..n} k * A327673(n,k).
MAPLE
b:= proc(n, i, k, p) option remember;
`if`(n=0, p!, `if`(i<1, 0, add(binomial(k^i, j)*
b(n-i*j, min(n-i*j, i-1), k, p+j)/j!, j=0..n/i)))
end:
a:= n-> add(add(k*b(n$2, i, 0)*(-1)^(k-i)*
binomial(k, i), i=0..k), k=0..n):
seq(a(n), n=0..23);
MATHEMATICA
b[n_, i_, k_, p_] := b[n, i, k, p] =
If[n == 0, p!, If[i < 1, 0, Sum[Binomial[k^i, j]*
b[n - i*j, Min[n - i*j, i - 1], k, p + j]/j!, {j, 0, n/i}]]];
a[n_] := Sum[Sum[k*b[n, n, i, 0]*(-1)^(k-i)*
Binomial[k, i], {i, 0, k}], {k, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Apr 11 2022, after Alois P. Heinz *)
CROSSREFS
Cf. A327673.
Sequence in context: A054932 A217240 A222834 * A338075 A394494 A177879
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 21 2019
STATUS
approved