A321908 - OEIS

%I #4 Nov 22 2018 05:21:40

%S 1,1,2,2,6,3,24,6,12,8,120,8,720,30,24,24,5040,24,40320,20,80,144,

%T 362880,30,144,840,144,72,3628800,45,39916800,120,360,5760,360,80,

%U 479001600,45360,2016,72,6227020800,144,87178291200,336,240,403200,1307674368000,144

%N If y is the integer partition with Heinz number n, then a(n) = |y|! / syt(y), where syt(y) is the number of standard Young tableaux of shape y.

%C a(n) is the LCM of the denominators of the coefficients in the expansion of Schur functions in terms of power sum symmetric functions.

%F a(n) = A056239(n)! / A153452(n).

%t syt[n_]:=If[n==1,1,Sum[syt[n/q*If[q==2,1,NextPrime[q,-1]]],{q,FactorInteger[n][[All,1]]}]];

%t Table[Total[Cases[FactorInteger[n],{p_,k_}:>k*PrimePi[p]]]!/syt[n],{n,30}]

%Y Cf. A000085, A008480, A056239, A082733, A153452, A296150, A296188, A300121, A304438, A317552, A317554, A321742-A321765, A321900, A321907.

%K nonn

%O 1,3

%A _Gus Wiseman_, Nov 21 2018