A136512 - OEIS

%I #6 Feb 29 2020 16:09:28

%S 1,2,4,12,64,616,10304,293744,14381056,1242433312,196990542848,

%T 59624929814720,35242762808786944,40573409794074305152,

%U 89317952471536946659328,368970766373159503907450624,2827862662172992194150488080384,40061570271801436240253461050024448,1050869620561002649814192493096912289792

%N Produced by same formula that gives A093934 (signed tournaments), but with LCM instead of GCD in the exponent.

%H Andrew Howroyd, <a href="/A136512/b136512.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = Sum_{j} (1/(Product (k^(j_k) (j_k)!))) * 2^{t_j},

%F where j runs through all partitions of n into odd parts, say with j_1 parts of size 1, j_3 parts of size 3, etc.,

%F and t_j = (1/2)*[ Sum_{r=1..n, s=1..n} j_r j_s lcm(r,s) + Sum_{r} j_r ].

%o (PARI)

%o permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

%o edges(v) = {sum(i=2, #v, sum(j=1, i-1, lcm(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}

%o oddp(v) = {for(i=1, #v, if(bitand(v[i], 1)==0, return(0))); 1}

%o a(n) = {my(s=0); forpart(p=n, if(oddp(p), s+=permcount(p)*2^(#p+edges(p)))); s/n!} \\ _Andrew Howroyd_, Feb 29 2020

%Y Cf. A093934.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jul 21 2009