A156291 Triangle read by rows: T(n,m) = Product_{k=1..n} Phi(k, m+1) where Phi(k,m) is the k-th cyclotomic polynomial evaluated at m.

1, 3, 8, 21, 104, 315, 105, 1040, 5355, 19344, 3255, 125840, 1826055, 15107664, 86590175, 9765, 880880, 23738715, 317260944, 2684295425, 16476602400, 1240155, 962801840, 129637122615, 6196423497264, 150285647959475, 2261529015616800, 23895819265962735

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Formula

T(n,m) = Product_{k=1..n} Phi(k, m + 1).

Example

Triangle begins:
  1;
  3, 8;
  21, 104, 315;
  105, 1040, 5355, 19344;
  3255, 125840, 1826055, 15107664, 86590175;
  9765, 880880, 23738715, 317260944, 2684295425, 16476602400;
  1240155, 962801840, 129637122615, 6196423497264, 150285647959475, 2261529015616800, 23895819265962735;
  ...

Mathematica

Clear[t, n, m, i, k];
t[n_, m_] = Product[Cyclotomic[k, m + 1], {k, 1, n}];
Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]

Prog

(PARI) T(n, m) = prod(k=1, n, polcyclo(k, m+1)); \\ Michel Marcus, Feb 08 2023

Crossrefs

Cf. A156173.

Sequence in context: A148769 A361574 A353424 * A111136 A374340 A348636

Adjacent sequences: A156288 A156289 A156290 * A156292 A156293 A156294

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Feb 07 2009

Extensions

Edited by Sean A. Irvine, Apr 13 2026

Status

approved