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A326654 Number of colored integer partitions of n using all colors of an initial interval of the color palette such that each block of part i with multiplicity j has a pattern of i*j colors in (weakly) increasing order; 2
1, 1, 4, 16, 70, 356, 1928, 11428, 69772, 471200, 3350320, 25067040, 195361800, 1559368544, 13165162256, 116528178688, 1074460079840, 10203335290992, 99238550358000, 979455883492672, 10002569256970848, 105957081274335392, 1164108439659208704 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add((t->

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

    end:

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

seq(a(n), n=0..25);

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n==0, 1, If[i < 1, 0, Sum[With[{t = i j}, b[n - t, Min[n - t, i - 1], k]*Binomial[k + t - 1, t]], {j, 0, n/i}]]];

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

a /@ Range[0, 25] (* Jean-Fran├žois Alcover, Dec 15 2020, after Alois P. Heinz *)

CROSSREFS

Row sums of A326500.

Sequence in context: A151244 A280767 A091354 * A246014 A231373 A161797

Adjacent sequences:  A326651 A326652 A326653 * A326655 A326656 A326657

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 12 2019

STATUS

approved

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Last modified May 28 04:02 EDT 2022. Contains 354112 sequences. (Running on oeis4.)