A153271 Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 3, read by rows.

5, 5, 30, 5, 35, 315, 5, 40, 440, 6160, 5, 45, 585, 9945, 208845, 5, 50, 750, 15000, 375000, 11250000, 5, 55, 935, 21505, 623645, 21827575, 894930575, 5, 60, 1140, 29640, 978120, 39124800, 1838865600, 99298742400, 5, 65, 1365, 39585, 1464645, 65909025, 3493178325, 213083877825, 14702787569925

Offset

0,1

Comments

Row sums are {5, 35, 355, 6645, 219425, 11640805, 917404295, 101177741765, 14919432040765, 2839006665525525, 677815000136926955, ...}.

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 3.

Example

Triangle begins as:
  5;
  5, 30;
  5, 35, 315;
  5, 40, 440,  6160;
  5, 45, 585,  9945, 208845;
  5, 50, 750, 15000, 375000, 11250000;
  5, 55, 935, 21505, 623645, 21827575, 894930575;

Maple

m:=3; seq(seq(`if`(k=0, ithprime(m), mul(j*n + ithprime(m), j=0..k)), k=0..n), n=0..10); # G. C. Greubel, Dec 03 2019

Mathematica

T[n_, k_, m_]:= If[k==0, Prime[m], Product[j*n + Prime[m], {j, 0, k}]];
Table[T[n, k, 3], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(PARI) T(n, k) = my(m=3); if(k==0, prime(m), prod(j=0, k, j*n + prime(m)) ); \\ G. C. Greubel, Dec 03 2019
(Magma) m:=3;
function T(n, k)
  if k eq 0 then return NthPrime(m);
  else return (&*[j*n + NthPrime(m): j in [0..k]]);
  end if; return T; end function;
[T(n, k): k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 03 2019
(Sage)
def T(n, k):
    m=3
    if (k==0): return nth_prime(m)
    else: return product(j*n + nth_prime(m) for j in (0..k))
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Dec 03 2019

Crossrefs

Cf. A153271 (m=2), this sequence (m=3), A153272 (m=4).

Sequences related to m values:

m=2: A001147, A001710, A008545, A032031, A047056, A144739, A144758.

m=3: A001720, A007696, A008543, A034000, A051577, A052562, A147585, A147625, A147629.

Sequence in context: A284140 A284182 A020551 * A261569 A117858 A365824

Adjacent sequences: A153268 A153269 A153270 * A153272 A153273 A153274

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 22 2008

Extensions

Edited by G. C. Greubel, Dec 03 2019

Status

approved