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

1,3

Comments

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

Links

Table of n, a(n) for n=1..48.

Formula

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

Mathematica

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}]

Crossrefs

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

Sequence in context: A296147 A130712 A276075 * A130728 A276085 A334870

Adjacent sequences: A321905 A321906 A321907 * A321909 A321910 A321911

Keyword

nonn

Author

Gus Wiseman, Nov 21 2018

Status

approved