A285175 Number of normal generalized Young tableaux, of shape the integer partition with Heinz number n, with all rows and columns strictly increasing.

1, 1, 1, 1, 1, 3, 1, 1, 3, 5, 1, 5, 1, 7, 11, 1, 1, 11, 1, 13, 23, 9, 1, 7, 11, 11, 11, 25, 1, 51, 1, 1, 39, 13, 45, 23, 1, 15, 59, 25, 1, 135, 1, 41, 73, 17, 1, 9, 45, 73, 83, 61, 1, 45, 107, 63, 111, 19, 1, 135, 1, 21, 259, 1, 205, 279, 1, 85, 143, 349, 1

Offset

1,6

Comments

A generalized Young tableau of shape y is an array obtained by replacing the dots in the Ferrers diagram of y with positive integers. 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).

Links

Table of n, a(n) for n=1..71.

Example

The a(15) = 11 tableaux:
1 2 3   1 2 4   1 3 4   1 2 5   1 3 5
4 5     3 5     2 5     3 4     2 4
.
1 2 3   1 2 3   1 2 4   1 2 4   1 3 4
2 4     3 4     2 3     3 4     2 4
.
1 2 3
2 3

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, Select[Rest[Divisors[n]], SquareFreeQ]}]];
Array[a, 100]

Crossrefs

Cf. A000085, A001221, A005117, A006958, A015128, A056239, A138178, A153452, A238690, A296150, A296188, A297388, A299925, A299926, A299968, A300118, A300120, A300122.

Sequence in context: A075001 A252840 A093803 * A016599 A079650 A094644

Adjacent sequences: A285172 A285173 A285174 * A285176 A285177 A285178

Keyword

nonn

Author

Gus Wiseman, Feb 26 2018

Status

approved