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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 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

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Last modified August 1 06:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)