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%I #9 Jun 27 2018 13:15:46
%S 1,1,3,3,9,21,46,95,273,363,731,3088,6247,24152,46012,319511,1141923,
%T 2138064,7346404,13530107,45297804,271446312
%N Number of triangles whose weight is the n-th Fermi-Dirac prime in the multiorder of integer partitions of Fermi-Dirac primes into Fermi-Dirac primes.
%C A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0. An FD-partition is an integer partition of a Fermi-Dirac prime into Fermi-Dirac primes. a(n) is the number of sequences of FD-partitions whose sums are weakly decreasing and sum to the n-th Fermi-Dirac prime.
%H Gus Wiseman, <a href="https://docs.google.com/document/d/1m0s6DGTBkDW9gvMuFmJHvy6oLGRAbQ7okAZcOPZawp0/pub">Comcategories and Multiorders</a>
%H Gus Wiseman, <a href="/A316220/a316220.png">Illustration of the first six terms of A316220.</a>
%t nn=60;
%t FDpQ[n_]:=With[{f=FactorInteger[n]},n>1&&Length[f]==1&&MatchQ[FactorInteger[2f[[1,2]]],{{2,_}}]];
%t FDpl=Select[Range[nn],FDpQ];
%t fen[n_]:=fen[n]=SeriesCoefficient[Product[1/(1-x^p),{p,Select[Range[n],FDpQ]}],{x,0,n}];
%t Table[Sum[Times@@fen/@p,{p,Select[IntegerPartitions[FDpl[[n]]],And@@FDpQ/@#&]}],{n,Length[FDpl]}]
%Y Cf. A050376, A063834, A064547, A213925, A269134, A281113, A299757, A305829, A316202, A316210, A316211, A316219, A316228.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Jun 26 2018
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