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A136512
Produced by same formula that gives A093934 (signed tournaments), but with LCM instead of GCD in the exponent.
1
1, 2, 4, 12, 64, 616, 10304, 293744, 14381056, 1242433312, 196990542848, 59624929814720, 35242762808786944, 40573409794074305152, 89317952471536946659328, 368970766373159503907450624, 2827862662172992194150488080384, 40061570271801436240253461050024448, 1050869620561002649814192493096912289792
OFFSET
0,2
FORMULA
a(n) = Sum_{j} (1/(Product (k^(j_k) (j_k)!))) * 2^{t_j},
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.,
and t_j = (1/2)*[ Sum_{r=1..n, s=1..n} j_r j_s lcm(r,s) + Sum_{r} j_r ].
PROG
(PARI)
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}
edges(v) = {sum(i=2, #v, sum(j=1, i-1, lcm(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}
oddp(v) = {for(i=1, #v, if(bitand(v[i], 1)==0, return(0))); 1}
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
CROSSREFS
Cf. A093934.
Sequence in context: A253832 A004400 A005831 * A137160 A217716 A129824
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 21 2009
STATUS
approved

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Last modified September 20 11:54 EDT 2024. Contains 376068 sequences. (Running on oeis4.)