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A326493 Sum of multinomials M(n-k; p_1-1, ..., p_k-1), where p = (p_1, ..., p_k) ranges over all partitions of n into distinct parts (k is a partition length). 3
1, 1, 1, 2, 2, 5, 9, 21, 38, 146, 322, 902, 3106, 8406, 35865, 123321, 393691, 1442688, 7310744, 23471306, 129918661, 500183094, 2400722981, 9592382321, 47764284769, 280267554944, 1247781159201, 7620923955225, 36278364107926, 189688942325418, 1124492015730891 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..731

Wikipedia, Multinomial coefficients

Wikipedia, Partition (number theory)

MAPLE

with(combinat):

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

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

seq(a(n), n=0..30);

# second Maple program:

b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, p!,

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

    end:

a:= n-> b(n$3):

seq(a(n), n=0..31);

CROSSREFS

Cf. A007837, A327711, A327712.

Sequence in context: A052969 A002990 A060405 * A003228 A184713 A110182

Adjacent sequences:  A326490 A326491 A326492 * A326494 A326495 A326496

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 22 2019

STATUS

approved

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Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)