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A327712 Sum of multinomials M(n-k; p_1-1, ..., p_k-1), where p = (p_1, ..., p_k) ranges over all compositions of n into distinct parts (k is a composition length). 3
1, 1, 1, 3, 3, 9, 29, 57, 135, 615, 2635, 6273, 25151, 82623, 525281, 2941047, 9100709, 38766777, 205155713, 902705793, 7714938567, 52987356783, 204844103977, 1042657233471, 5520661314689, 38159472253821, 211945677298567, 2404720648663335, 19773733727088813 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..706

Wikipedia, Multinomial coefficients

Wikipedia, Partition (number theory)

MAPLE

with(combinat):

a:= n-> add(multinomial(n-nops(p), map(x-> x-1, p)[], 0), p=map(h->

    permute(h)[], select(l-> nops(l)=nops({l[]}), partition(n)))):

seq(a(n), n=0..28);

# second Maple program:

a:= proc(m) option remember; local b; b:=

      proc(n, i, j) option remember; `if`(i*(i+1)/2>=n,

       `if`(n=0, (m-j)!*j!, b(n, i-1, j)+

        b(n-i, min(n-i, i-1), j+1)/(i-1)!), 0)

      end: b(m$2, 0):

    end:

seq(a(n), n=0..28);

MATHEMATICA

a[m_] := a[m] = Module[{b}, b[n_, i_, j_] := b[n, i, j] = If[i(i + 1)/2 >= n, If[n == 0, (m - j)! j!, b[n, i - 1, j] + b[n - i, Min[n - i, i - 1], j + 1]/(i - 1)!], 0]; b[m, m, 0]];

a /@ Range[0, 28] (* Jean-Fran├žois Alcover, May 10 2020, after 2nd Maple program *)

CROSSREFS

Cf. A026898, A326493, A327711.

Sequence in context: A117976 A010098 A029857 * A257611 A268617 A264412

Adjacent sequences:  A327709 A327710 A327711 * A327713 A327714 A327715

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 22 2019

STATUS

approved

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Last modified July 15 02:31 EDT 2020. Contains 335762 sequences. (Running on oeis4.)