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A285175 Number of normal generalized Young tableaux, of shape the integer partition with Heinz number n, with all rows and columns strictly increasing. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 19 15:37 EST 2020. Contains 331049 sequences. (Running on oeis4.)