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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.
3
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, ...}.
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).
Sequence in context: A203066 A165425 A220079 * A117860 A367456 A360367
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Dec 22 2008
EXTENSIONS
Edited by G. C. Greubel, Dec 03 2019
STATUS
approved