A321907 -id:A321907 - cp's OEIS frontend

A321908 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.

1, 1, 2, 2, 6, 3, 24, 6, 12, 8, 120, 8, 720, 30, 24, 24, 5040, 24, 40320, 20, 80, 144, 362880, 30, 144, 840, 144, 72, 3628800, 45, 39916800, 120, 360, 5760, 360, 80, 479001600, 45360, 2016, 72, 6227020800, 144, 87178291200, 336, 240, 403200, 1307674368000, 144

Offset: 1

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Gus Wiseman, Nov 21 2018

nonn

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

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

syt[n_]:=If[n==1,1,Sum[syt[n/q*If[q==2,1,NextPrime[q,-1]]],{q,FactorInteger[n][[All,1]]}]];
Table[Total[Cases[FactorInteger[n],{p_,k_}:>k*PrimePi[p]]]!/syt[n],{n,30}]

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

cp's OEIS Frontend

A321908 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.

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