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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A324122

Adjacent sequences:  A321905 A321906 A321907 * A321909 A321910 A321911

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 21 2018

STATUS

approved

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Last modified April 22 22:22 EDT 2019. Contains 322378 sequences. (Running on oeis4.)