A156291 A triangle sequence of Cyclotomic products: t(n,m)=Product[Cyclotomic[k, m + 1], {k, 1, n}].

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

Comments

Row sums are: {1, 11, 440, 25844, 103652989, 19502788129, 26313960954200884, 1365438215011770727764, 13180641383420867649481463463, 2480700284650078006965956163001113,...}.

Links

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

Formula

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

Example

{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 A348636 A063937

Adjacent sequences: A156288 A156289 A156290 * A156292 A156293 A156294

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Feb 07 2009

Status

approved