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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 (list; graph; refs; listen; history; text; internal format)
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 n-th 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/(1-x^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

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Last modified September 18 18:59 EDT 2021. Contains 347533 sequences. (Running on oeis4.)