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A327556
Number of colored integer partitions of 2n using all colors of an n-set such that all parts have different color patterns and a pattern for part i has i colors in (weakly) increasing order.
2
1, 1, 15, 319, 10305, 456540, 26189661, 1870454452, 161632399892, 16535827882568, 1968749174314009, 269023182822761584, 41709476698204311667, 7266527579101535573799, 1410853257166617346437587, 303111227353456160724127886, 71611509245127165374518157052
OFFSET
0,3
LINKS
FORMULA
a(n) = A327116(2n,n).
MAPLE
C:= binomial:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
b(n-i*j, min(n-i*j, i-1), k)*C(C(k+i-1, i), j), j=0..n/i)))
end:
a:= n-> add(b(2*n$2, i)*(-1)^(n-i)*C(n, i), i=0..n):
seq(a(n), n=0..17);
MATHEMATICA
c = Binomial;
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, Min[n - i*j, i - 1], k] c[c[k + i - 1, i], j], {j, 0, n/i}]]];
a[n_] := Sum[b[2n, 2n, i] (-1)^(n - i) c[n, i], {i, 0, n}];
a /@ Range[0, 17] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)
CROSSREFS
Cf. A327116.
Sequence in context: A062757 A088913 A053102 * A132392 A131699 A077738
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2019
STATUS
approved