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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

%I

%S 1,1,1,2,2,5,9,21,38,146,322,902,3106,8406,35865,123321,393691,

%T 1442688,7310744,23471306,129918661,500183094,2400722981,9592382321,

%U 47764284769,280267554944,1247781159201,7620923955225,36278364107926,189688942325418,1124492015730891

%N 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).

%H Alois P. Heinz, <a href="/A326493/b326493.txt">Table of n, a(n) for n = 0..731</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients">Multinomial coefficients</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>

%p with(combinat):

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

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

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

%p # second Maple program:

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

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

%p end:

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

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

%Y Cf. A007837, A327711, A327712.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Sep 22 2019

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Last modified September 24 07:27 EDT 2020. Contains 337317 sequences. (Running on oeis4.)