A136512 Produced by same formula that gives A093934 (signed tournaments), but with LCM instead of GCD in the exponent.

1, 2, 4, 12, 64, 616, 10304, 293744, 14381056, 1242433312, 196990542848, 59624929814720, 35242762808786944, 40573409794074305152, 89317952471536946659328, 368970766373159503907450624, 2827862662172992194150488080384, 40061570271801436240253461050024448, 1050869620561002649814192493096912289792

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

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

Adjacent sequences: A136509 A136510 A136511 * A136513 A136514 A136515

Keyword

nonn

Author

N. J. A. Sloane, Jul 21 2009

Status

approved