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A130721
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Sum of the cubes of the number of standard Young tableaux over all partitions of n.
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0
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1, 1, 2, 10, 64, 596, 8056, 130432, 2534960, 59822884, 1718480368, 56754444440
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The sum of the zeroth power of the number f(p) of standard Young tableaux gives the partition function (A000041), the sum of the first power of f(p) gives the involution function (A000085), the sum of the squares of f(p) gives the factorial function (A000142), so this sequence is the natural one after them.
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FORMULA
| For p a partition of n, let f(p) be the number of standard Young tableaux with shape p. Then a(n) = sum(f(p)^3) where the sum ranges over all partitions p of n.
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EXAMPLE
| a(4) = 1^3 + 3^3 + 2^3 + 3^3 + 1^3 because the five partitions of 4 (namely 4, 3+1, 2+2, 2+1+1, 1+1+1+1) have respectively 1, 3, 2, 3, 1 standard Young tableaux.
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CROSSREFS
| Cf. A000041, A000085, A000142.
Sequence in context: A129130 A186268 A078531 * A167449 A064170 A151410
Adjacent sequences: A130718 A130719 A130720 * A130722 A130723 A130724
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KEYWORD
| nonn
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AUTHOR
| David A. Madore (david.madore(AT)ens.fr), Jul 03 2007
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