A156173 A q-factorial type triangle sequence: t(n,m)=Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}].

1, 3, 4, 21, 52, 105, 315, 2080, 8925, 29016, 9765, 251680, 3043425, 22661496, 121226245, 615195, 91611520, 4154275125, 88515803376, 1131162092095, 10017774259200, 78129765, 100131391360, 22686496457625, 1728802155736656

Offset

1,2

Comments

Row sums are:

{1, 7, 178, 40336, 147192611, 11241698656511, 21625231505212231436,

1226764024087113751074788856, 2355209486831128977237340079226283377,

172888169716515661763262995345027335509897708987,...}.

Links

Table of n, a(n) for n=1..25.

John Shareshian, Michelle L. Wachs, q-Eulerian Polynomials : Excedance Number ans Major Index, arXiv: math/ 0608274v1, 11 Aug 2006, page 3.

Formula

t(n,m)=Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}].

Example

{1},
{3, 4},
{21, 52, 105},
{315, 2080, 8925, 29016},
{9765, 251680, 3043425, 22661496, 121226245},
{615195, 91611520, 4154275125, 88515803376, 1131162092095, 10017774259200},
{78129765, 100131391360, 22686496457625, 1728802155736656, 63330372050122765, 1375009641495014400, 20185139902805378865},
{19923090075, 328430963660800, 495586515116818125, 168827903320618878336, 21274128570193389587095, 1321109263548409835520000, 48378633136349277767794425, 1177042838234827583459440000},
{10180699028325, 3232089113385932800, 43304845277422684580625, 82435457461295106532780416, 42878835824239014254983869205, 8885253784030448738183147520000, 927610024989668734297857360967425, 57001313848230245122464621625840000, 2297271634742810443154153338805764581},
{10414855105976475, 95424198983606279987200, 15136126045591163828042953125, 201258420458750640859769304304896, 518543838148941095553869851505328175, 418310711031156574478261944188764160000, 142287668466497494704440569679875994730825, 24843911488189148287648216529610193612000000, 2552524038347870310755413660544832496799359491, 170310659060181679663863033233125976844488908800}

Mathematica

Clear[t, n, m, i, k];
t[n_, m_] = Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}];
Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
(* Second program: *)
T[n_, m_] := QFactorial[n, m + 1];
Table[T[n, m], {n, 1, 7}, {m, 1, n}] // Flatten (* Jean-François Alcover, Jan 18 2019 *)

Crossrefs

Sequence in context: A225478 A254884 A034475 * A094632 A081698 A182096

Adjacent sequences: A156170 A156171 A156172 * A156174 A156175 A156176

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Feb 05 2009

Status

approved