0,3

The sum of the zero-th 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.

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.

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.

Cf. A000041, A000085, A000142.

Sequence in context: A141140 A129130 A078531 this_sequence A064170 A151410 A027307

Adjacent sequences: A130718 A130719 A130720 this_sequence A130722 A130723 A130724

nonn

David A. Madore (david.madore(AT)ens.fr), Jul 03 2007