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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 (list; table; graph; refs; listen; history; text; internal format)
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 A274908 A009201

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

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)