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A009692 Number of partitions of {1, 2, ..., 2n} into pairs whose differences are primes.

%I A009692 #23 Mar 01 2021 10:15:59
%S A009692 1,0,1,3,10,40,153,921,5144,30717,230748,1766056,14052445,116580521,
%T A009692 897876519,7657321097,75743979608,788733735080,7569825650083,
%U A009692 75242386295617,831978453306391,9444103049405370,120064355466770831,1579842230380587833
%N A009692 Number of partitions of {1, 2, ..., 2n} into pairs whose differences are primes.
%e A009692 a(3) = 3: {{1,6}, {2,4}, {3,5}}, {{1,4}, {2,5}, {3,6}}, {{1,3}, {2,5}, {4,6}}. - _Alois P. Heinz_, Nov 15 2016
%p A009692 b:= proc(s) option remember; `if`(s={}, 1, (j-> add(`if`(i<j
%p A009692       and isprime(j-i), b(s minus {i, j}), 0), i=s))(max(s)))
%p A009692     end:
%p A009692 a:= n-> b({$1..2*n}):
%p A009692 seq(a(n), n=0..12);  # _Alois P. Heinz_, Nov 15 2016
%t A009692 b[s_] := b[s] = If[s == {}, 1, Function[j, Sum[If[i < j && PrimeQ[j - i], b[s ~Complement~ {i, j}], 0], {i, s}]][Max[s]]];
%t A009692 a[n_] := b[Range[2n]];
%t A009692 Table[Print[n, " ", a[n]]; a[n], {n, 0, 18}] (* _Jean-François Alcover_, Mar 01 2021, after _Alois P. Heinz_ *)
%Y A009692 Cf. A000341.
%K A009692 nonn,hard
%O A009692 0,4
%A A009692 _David W. Wilson_
%E A009692 a(0), a(14)-a(18) from _Alois P. Heinz_, Nov 15 2016
%E A009692 a(19)-a(23) from _Bert Dobbelaere_, Feb 20 2020