A296560 Number of normal semistandard Young tableaux whose shape is the conjugate of the integer partition with Heinz number n.

1, 1, 1, 2, 1, 4, 1, 4, 6, 6, 1, 12, 1, 8, 16, 8, 1, 28, 1, 24, 30, 10, 1, 32, 22, 12, 44, 40, 1, 96, 1, 16, 48, 14, 68, 96, 1, 16, 70, 80, 1, 220, 1, 60, 204, 18, 1, 80, 90, 168, 96, 84, 1, 224, 146, 160, 126, 20, 1, 400, 1, 22, 584, 32, 264, 416, 1, 112, 160

Offset: 1

Author

Gus Wiseman, Feb 15 2018

Keywords

• nonn

Comments

A tableau is normal if its entries span an initial interval of positive integers. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Crossrefs

Cf. A000085, A001222, A056239, A063834, A112798, A122111, A138178, A153452, A191714, A210391, A228125, A296150, A296188, A299202.

Programs

Mathematica

a[n_]:=If[n===1,1,Sum[a[n/q*Times@@Cases[FactorInteger[q],{p_,k_}:>If[p===2,1,NextPrime[p,-1]^k]]],{q,Rest[Divisors[n]]}]];
Array[a,100]