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A327729 a(n) = Sum_{p} M(n-k; p_1-1, ..., p_k-1) * Product_{j=1..k} a(p_j), where p = (p_1, ..., p_k) ranges over all partitions of n into smaller parts (k is a partition length and M is a multinomial). 3
1, 1, 2, 6, 18, 90, 414, 2892, 18342, 155124, 1265130, 13413240, 129656286, 1564538796, 18285385518, 255345207156, 3378398348214, 52931303772912, 797460543143154, 13926097774972152, 234050020177159926, 4466082284967035124, 83159771376289666806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The formula is a generalization of the formula given in A327643.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..460

Wikipedia, Multinomial coefficients

Wikipedia, Partition (number theory)

MAPLE

with(combinat):

a:= proc(n) option remember; `if`(n<2, 1, add(mul(a(i), i=p)

      *multinomial(n-nops(p), map(x-> x-1, p)[]),

       p=select(x-> nops(x)>1, partition(n))))

    end:

seq(a(n), n=1..24);

# second Maple program:

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

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

    end:

a:= n-> `if`(n<2, 1, b(n$2, n-1)):

seq(a(n), n=1..24);

CROSSREFS

Cf. A327643, A327711.

Sequence in context: A007869 A263915 A144557 * A273001 A118455 A165774

Adjacent sequences:  A327726 A327727 A327728 * A327730 A327731 A327732

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 23 2019

STATUS

approved

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Last modified February 23 11:52 EST 2020. Contains 332159 sequences. (Running on oeis4.)