OFFSET
1,3
COMMENTS
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.
LINKS
Gus Wiseman, Comcategories and Multiorders
Gus Wiseman, Illustration of the first six terms of A316220.
MATHEMATICA
nn=60;
FDpQ[n_]:=With[{f=FactorInteger[n]}, n>1&&Length[f]==1&&MatchQ[FactorInteger[2f[[1, 2]]], {{2, _}}]];
FDpl=Select[Range[nn], FDpQ];
fen[n_]:=fen[n]=SeriesCoefficient[Product[1/(1-x^p), {p, Select[Range[n], FDpQ]}], {x, 0, n}];
Table[Sum[Times@@fen/@p, {p, Select[IntegerPartitions[FDpl[[n]]], And@@FDpQ/@#&]}], {n, Length[FDpl]}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 26 2018
STATUS
approved