A153272 Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 4, read by rows.

7, 7, 56, 7, 63, 693, 7, 70, 910, 14560, 7, 77, 1155, 21945, 504735, 7, 84, 1428, 31416, 848232, 27143424, 7, 91, 1729, 43225, 1339975, 49579075, 2131900225, 7, 98, 2058, 57624, 2016840, 84707280, 4150656720, 232436776320, 7, 105, 2415, 74865, 2919735, 137227545, 7547514975, 475493443425, 33760034483175

Offset

0,1

Comments

Row sums are {7, 63, 763, 15547, 527919, 28024591, 2182864327, 236674216947, 34243215666247, 6391699984166119, 1497639790982770659, ...}.

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 = 4.

Example

Triangle begins as:
  7;
  7, 56;
  7, 63,  693;
  7, 70,  910, 14560;
  7, 77, 1155, 21945,  504735;
  7, 84, 1428, 31416,  848232, 27143424;
  7, 91, 1729, 43225, 1339975, 49579075, 2131900225;

Maple

m:=4; 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, 4], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(PARI) T(n, k) = my(m=4); if(k==0, prime(m), prod(j=0, k, j*n + prime(m)) ); \\ G. C. Greubel, Dec 03 2019
(Magma) m:=4;
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=4
    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. A153270 (m=2), A153271 (m=3), this sequence (m=4).

Cf. A001730, A051579, A051604.

Sequence in context: A203066 A165425 A220079 * A117860 A367456 A360367

Adjacent sequences: A153269 A153270 A153271 * A153273 A153274 A153275

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 22 2008

Extensions

Edited by G. C. Greubel, Dec 03 2019

Status

approved