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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);

CROSSREFS

Cf. A327245.

Sequence in context: A158768 A139191 A319490 * A176073 A145619 A027490

Adjacent sequences:  A327585 A327587 A327588 * A327590 A327591 A327592

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 17 2019

STATUS

approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)