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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
0, 1, 7, 62, 642, 7784, 108824, 1725072, 30605384, 601213744, 12958778704, 304145108160, 7722286425312, 210920029636224, 6166996162239840, 192199468584942816, 6360760834966301120, 222782888877269937664, 8233066075880951824000, 320162458265691237967360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

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

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

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

CROSSREFS

Cf. A327245.

Sequence in context: A171078 A180776 A024089 * A287481 A289212 A060005

Adjacent sequences:  A327585 A327586 A327587 * A327589 A327590 A327591

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 17 2019

STATUS

approved

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Last modified November 30 13:47 EST 2021. Contains 349420 sequences. (Running on oeis4.)