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A066117 Triangle read by rows: T(n,k) = T(n-1,k-1)*T(n,k-1) and T(n,1) = prime(n). 8
2, 3, 6, 5, 15, 90, 7, 35, 525, 47250, 11, 77, 2695, 1414875, 66852843750, 13, 143, 11011, 29674645, 41985913344375, 2806877704512541816406250, 17, 221, 31603, 347980633, 10326201751150285, 433555011900329243987584396875 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..27.

Index entries for triangles and arrays related to Pascal's triangle

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).

A(row,1) = A007188(row-1), for col > 1, A(row,col) = A003961(A(row,col-1)).

For all row >= 1, col >= 1, A055396(A(row,col)) = col.

(End)

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-Fran├žois Alcover, Nov 13 2017 *)

PROG

(Scheme)

(define (A066117 n) (A066117bi (A002260 n) (A004736 n)))

;; 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:

(define (A066117bi row col) (if (= 1 col) (A007188 (- row 1)) (A003961 (A066117bi row (- col 1)))))

;; Antti Karttunen, Sep 18 2016

CROSSREFS

Cf. A000040, A006094 and A066116 (three leftmost diagonal of triangular table = three topmost rows of square array).

Cf. A007188, A267096 (two rightmost diagonals of the triangular table = two leftmost columns of square array).

Cf. A003961, A055396.

Cf. A064319, A066119.

Cf. also A099884, A255483, A276586, A276588 (other arrays derived from this one).

Sequence in context: A276942 A255483 A098012 * A222311 A156833 A319344

Adjacent sequences:  A066114 A066115 A066116 * A066118 A066119 A066120

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Dec 05 2001

STATUS

approved

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Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)