OFFSET
1,1
COMMENTS
As a square array read by descending antidiagonals, A(n, k), n >= 1, k >= 1, gives the encoding defined in A297845 of the polynomial (x+1)^(n-1) * x^(k-1). - Peter Munn, Jul 27 2022
LINKS
FORMULA
From Antti Karttunen, Sep 19 2016: (Start)
When computed as a square array A(row,col), row >= 1, col >= 1:
A(1,col) = A000040(col), for row > 1, A(row,col) = A(row-1,col)*A(row-1,col+1).
For all row >= 1, col >= 1, A055396(A(row,col)) = col.
(End)
A(1,1) = 2; for n > 1, A(n,k) = A297845(A(n-1,k),6); for k > 1, A(n,k) = A297845(A(n,k-1),3). - Peter Munn, Jul 20 2022
EXAMPLE
T(4,3) = T(3,2)*T(4,2) = 15*35 = 525. Rows start
2;
3, 6;
5, 15, 90;
7, 35, 525, 47250;
...
From Antti Karttunen, Sep 18 2016: (Start)
Alternatively, this table can be viewed as a square array. Then the top left 5x4 corner looks as:
2, 3, 5, 7, 11
6, 15, 35, 77, 143
90, 525, 2695, 11011, 31603
47250, 1414875, 29674645, 347980633, 2255916949
(End)
MATHEMATICA
T[n_, 1] := Prime[n];
T[n_, k_] := T[n, k] = T[n - 1, k - 1]*T[n, k - 1];
Table[T[n, k], {n, 1, 7}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 13 2017 *)
PROG
(Scheme)
;; Compute as a square array, with row >= 1, col >= 1:
(define (A066117bi row col) (if (= 1 row) (A000040 col) (* (A066117bi (- row 1) col) (A066117bi (- row 1) (+ col 1)))))
;; With alternative recurrence:
;; Antti Karttunen, Sep 18 2016
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Dec 05 2001
STATUS
approved