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 A327589 Number of colored compositions of 2n using all colors of an n-set such that all parts have different color patterns and the patterns for parts i have i colors in (weakly) increasing order. 2
 1, 1, 39, 2272, 284319, 56455146, 16786728000, 6935657012558, 3810209706509775, 2684955985258788274, 2361563245536690165774, 2535933313556764621139740, 3265213763332455703665035736, 4965602758384602312429712415116, 8805913731971382862369182854094726 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..190 (terms 0..120 from Alois P. Heinz) FORMULA a(n) = A327245(2n,n). a(n) ~ c * d^n * n^(2*n), where d = 1.31520176578651896001... and c = 1.569966657460754514... - Vaclav Kotesovec, Sep 19 2019 MAPLE C:= binomial: b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add( b(n-i*j, min(n-i*j, i-1), k, p+j)*C(C(k+i-1, i), j), j=0..n/i))) end: a:= n-> add(b(2*n\$2, i, 0)*(-1)^(n-i)*C(n, i), i=0..n): seq(a(n), n=0..15); MATHEMATICA c = Binomial; b[n_, i_, k_, p_] := b[n, i, k, p] = If[n == 0, p!, If[i < 1, 0, Sum[ b[n-i*j, Min[n-i*j, i-1], k, p+j]*c[c[k+i-1, i], j], {j, 0, n/i}]]]; a[n_] := Sum[b[2n, 2n, i, 0]*(-1)^(n-i)*c[n, i], {i, 0, n}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Apr 11 2022, after Alois P. Heinz *) CROSSREFS Cf. A327245. Sequence in context: A158768 A139191 A319490 * A176073 A145619 A027490 Adjacent sequences: A327586 A327587 A327588 * A327590 A327591 A327592 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 17 2019 STATUS approved

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Last modified September 10 06:17 EDT 2024. Contains 375773 sequences. (Running on oeis4.)