OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..108
V. Kotesovec, Non-attacking chess pieces, 6ed, p.373-381
FORMULA
Asymptotic (V. Kotesovec, Oct 15 2011): a(n) ~ n^(2n)/n!*exp(-3/2).
MATHEMATICA
permopak[part_, k_]:=(hist=ConstantArray[0, k];
Do[hist[[part[[t]]]]++, {t, 1, Length[part]}];
(Length[part])!/Product[(hist[[t]])!, {t, 1, k}]);
waz1n[k_, n_]:=(If[n-k+1<k, 0, Binomial[n-k+1, k]]);
semiwaz[k_, n_]:=(psum=0;
Do[p=IntegerPartitions[k, {size}];
psum=psum+Sum[permopak[p[[i]], k]*Binomial[n, Length[p[[i]]]]*Product[waz1n[p[[i, j]], n] , {j, 1, Length[p[[i]]]}], {i, 1, Length[p]}], {size, 1, n}];
psum);
Table[semiwaz[n, n], {n, 1, 25}]
CROSSREFS
KEYWORD
nonn,nice,hard
AUTHOR
Vaclav Kotesovec, Oct 20 2011
STATUS
approved