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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)