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A327588 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 have i colors in (weakly) increasing order. 2

%I

%S 0,1,7,62,642,7784,108824,1725072,30605384,601213744,12958778704,

%T 304145108160,7722286425312,210920029636224,6166996162239840,

%U 192199468584942816,6360760834966301120,222782888877269937664,8233066075880951824000,320162458265691237967360

%N 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 have i colors in (weakly) increasing order.

%H Alois P. Heinz, <a href="/A327588/b327588.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = Sum_{k=1..n} k * A327245(n,k).

%p C:= binomial:

%p b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(

%p b(n-i*j, min(n-i*j, i-1), k, p+j)*C(C(k+i-1, i), j), j=0..n/i)))

%p end:

%p a:= n-> add(k*add(b(n$2, i, 0)*(-1)^(k-i)*C(k, i), i=0..k), k=0..n):

%p seq(a(n), n=0..21);

%Y Cf. A327245.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 17 2019

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Last modified January 21 00:46 EST 2022. Contains 350473 sequences. (Running on oeis4.)