

A316219


Number of triangles of weight prime(n) in the multiorder of integer partitions of prime numbers into prime parts.


5



1, 1, 3, 6, 15, 31, 92, 161, 464, 2347, 3987, 18202, 50136, 81722, 214976, 903048, 3684567, 5842249, 23206424, 57341256
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OFFSET

1,3


COMMENTS

A prime partition is an integer partition of a prime number into prime parts. Then a(n) is the number of sequences of prime partitions whose sums are weakly decreasing and sum to the nth prime number.


LINKS

Table of n, a(n) for n=1..20.
Gus Wiseman, Comcategories and Multiorders
Gus Wiseman, Illustration of the first five terms of A316219.


MATHEMATICA

nn=20;
pen[n_]:=pen[n]=SeriesCoefficient[Product[1/(1x^p), {p, Select[Range[n], PrimeQ]}], {x, 0, n}]
Table[Sum[Times@@pen/@p, {p, Select[IntegerPartitions[Prime[n]], And@@PrimeQ/@#&]}], {n, nn}]


CROSSREFS

Cf. A000040, A000041, A000607, A056768, A063834, A100118, A269134, A281113, A316220.
Sequence in context: A244711 A244712 A006961 * A034740 A323936 A305839
Adjacent sequences: A316216 A316217 A316218 * A316220 A316221 A316222


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jun 26 2018


STATUS

approved



