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A258566 Triangle in which n-th row contains all possible products of n-1 of the first n primes in descending order. 1
1, 3, 2, 15, 10, 6, 105, 70, 42, 30, 1155, 770, 462, 330, 210, 15015, 10010, 6006, 4290, 2730, 2310, 255255, 170170, 102102, 72930, 46410, 39270, 30030, 4849845, 3233230, 1939938, 1385670, 881790, 746130, 570570, 510510 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Triangle read by rows, truncated rows of the array in A185973.

Reversal of A077011.

LINKS

Table of n, a(n) for n=1..36.

FORMULA

T(1,1) = 1, T(n,k) = A000040(n)*T(n-1,k) for k < n, T(n,n) = A000040(n-1) * T(n-1,n-1).

EXAMPLE

Triangle begins:

      1;

      3,     2;

     15,    10,    6;

    105,    70,   42,   30;

   1155,   770,  462,  330,  210;

  15015, 10010, 6006, 4290, 2730, 2310;

MAPLE

T:= n-> (m-> seq(m/ithprime(j), j=1..n))(mul(ithprime(i), i=1..n)):

seq(T(n), n=1..10);  # Alois P. Heinz, Jun 18 2015

MATHEMATICA

T[1, 1] = 1; T[n_, n_] := T[n, n] = Prime[n-1]*T[n-1, n-1];

T[n_, k_] := T[n, k] = Prime[n]*T[n-1, k];

Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, May 26 2016 *)

CROSSREFS

Row sums: A024451.

T(n,1) = A070826(n).

T(n,n) = A002110(n-1).

For 2 <= n <= 9, T(n,2) = A118752(n-2). [corrected by Peter Munn, Jan 13 2018]

T(n,k) = A121281(n,k), but the latter has an extra column (0).

Cf. A077011, A185973, A286947.

Sequence in context: A218969 A345291 A185973 * A051917 A302845 A291251

Adjacent sequences:  A258563 A258564 A258565 * A258567 A258568 A258569

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Jun 03 2015

STATUS

approved

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Last modified November 27 09:19 EST 2021. Contains 349365 sequences. (Running on oeis4.)