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URL: https://oeis.org/A153270

⇱ A153270 - OEIS

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A153270
Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 2, read by rows.
2
3, 3, 12, 3, 15, 105, 3, 18, 162, 1944, 3, 21, 231, 3465, 65835, 3, 24, 312, 5616, 129168, 3616704, 3, 27, 405, 8505, 229635, 7577955, 295540245, 3, 30, 510, 12240, 379440, 14418720, 648842400, 33739804800, 3, 33, 627, 16929, 592515, 25478145, 1299385395, 76663738305, 5136470466435
OFFSET
0,1
COMMENTS
Row sums are {3, 15, 123, 2127, 69555, 3751827, 303356775, 34403458143, 5214459678387, 1018396843935195, 249088654250968899, ...}.
FORMULA
T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 2.
EXAMPLE
Triangle begins as:
3;
3, 12;
3, 15, 105;
3, 18, 162, 1944;
3, 21, 231, 3465, 65835;
3, 24, 312, 5616, 129168, 3616704;
3, 27, 405, 8505, 229635, 7577955, 295540245;
3, 30, 510, 12240, 379440, 14418720, 648842400, 33739804800;
MAPLE
m:=2; 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, 2], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(PARI) T(n, k) = my(m=2); if(k==0, prime(m), prod(j=0, k, j*n + prime(m)) ); \\ G. C. Greubel, Dec 03 2019
(Magma) m:=2;
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
(SageMath)
def T(n, k):
m=2
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. this sequence (m=2), A153271 (m=3), A153272 (m=4).
Sequence in context: A163372 A349922 A066437 * A065957 A303309 A268774
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Dec 22 2008
EXTENSIONS
Edited by G. C. Greubel, Dec 03 2019
STATUS
approved