login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327680 Total number of colors used in all colored integer partitions of n using all colors of an initial interval of the color palette such that parts i have distinct color patterns in arbitrary order and each pattern for a part i has i colors in (weakly) increasing order. 2
0, 1, 7, 44, 358, 2904, 29112, 296448, 3520568, 43482208, 602603120, 8712724080, 138736978208, 2302036052128, 41417364992160, 776413790063328, 15597709327298944, 325945020056535968, 7238587734613470208, 166897326948551436384, 4061690336695535982048 (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 * A309973(n,k).

MAPLE

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)*

       binomial(binomial(k+i-1, i), j)*j!, j=0..n/i)))

    end:

a:= n-> add(add(k*b(n$2, i)*(-1)^(k-i)*

        binomial(k, i), i=0..k), k=0..n):

seq(a(n), n=0..22);

MATHEMATICA

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] Binomial[Binomial[k+i-1, i], j] j!, {j, 0, n/i}]]];

a[n_] := Sum[Sum[k b[n, n, i](-1)^(k-i)Binomial[k, i], {i, 0, k}], {k, 0, n}];

a /@ Range[0, 22] (* Jean-Fran├žois Alcover, Dec 18 2020, after_Alois P. Heinz_ *)

CROSSREFS

Cf. A309973.

Sequence in context: A091127 A166775 A221541 * A156374 A171493 A262772

Adjacent sequences:  A327677 A327678 A327679 * A327681 A327682 A327683

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 21 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 25 22:37 EST 2021. Contains 341618 sequences. (Running on oeis4.)