%I #22 Aug 25 2021 07:01:37

%S 1,0,0,0,1,2,6,10,22,101,66,504,2088,3572,14398,49984,108030,191228,

%T 1087758,5005440,14081453,97492234,160186634,939652634,3926077642,

%U 4273706733,41832174879,214185383046,494248121522,6153003414039,38125026176659,13635112709648,39350572537836,511502485322923,1069875349612147,5075263842958032

%N Number of partitions of [2n] into pairs whose sums and differences are primes.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%e a(4) = 1: {{1,6}, {2,5}, {3,8}, {4,7}}.

%e a(5) = 2: {{1,6}, {2,9}, {3,10}, {4,7}, {5,8}}, {{1,6}, {2,5}, {3,8}, {4,9}, {7,10}}.

%p b:= proc(s) option remember; `if`(s={}, 1, (j-> add(`if`(i<j and

%p andmap(isprime, [j+i, j-i]), b(s minus {i, j}), 0), i=s))(max(s)))

%p end:

%p a:= n-> b({$1..2*n}):

%p seq(a(n), n=0..15);

%t b[s_] := b[s] = If[s == {}, 1, With[{j = Max[s]}, Sum[If[i < j && AllTrue[{j+i, j-i}, PrimeQ], b[s ~Complement~ {i, j}], 0], {i, s}]]];

%t a[n_] := b[Range[2n]];

%t a /@ Range[0, 15] (* _Jean-François Alcover_, Aug 25 2021, after _Alois P. Heinz_ *)

%Y Cf. A000341, A009692, A342139, A342155.

%K nonn

%O 0,6

%A _Alois P. Heinz_, Mar 01 2021

%E a(25)-a(35) from _Bert Dobbelaere_, Mar 06 2021