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

%I A156173 #10 Jan 18 2019 09:58:37
%S A156173 1,3,4,21,52,105,315,2080,8925,29016,9765,251680,3043425,22661496,
%T A156173 121226245,615195,91611520,4154275125,88515803376,1131162092095,
%U A156173 10017774259200,78129765,100131391360,22686496457625,1728802155736656
%N A156173 A q-factorial type triangle sequence: t(n,m)=Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}].
%C A156173 Row sums are:
%C A156173 {1, 7, 178, 40336, 147192611, 11241698656511, 21625231505212231436,
%C A156173 1226764024087113751074788856, 2355209486831128977237340079226283377,
%C A156173 172888169716515661763262995345027335509897708987,...}.
%H A156173 John Shareshian, Michelle L. Wachs, <a href="http://arxiv.org/abs/math/0608274">q-Eulerian Polynomials : Excedance Number ans Major Index</a>, arXiv: math/ 0608274v1, 11 Aug 2006, page 3.
%F A156173 t(n,m)=Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}].
%e A156173 {1},
%e A156173 {3, 4},
%e A156173 {21, 52, 105},
%e A156173 {315, 2080, 8925, 29016},
%e A156173 {9765, 251680, 3043425, 22661496, 121226245},
%e A156173 {615195, 91611520, 4154275125, 88515803376, 1131162092095, 10017774259200},
%e A156173 {78129765, 100131391360, 22686496457625, 1728802155736656, 63330372050122765, 1375009641495014400, 20185139902805378865},
%e A156173 {19923090075, 328430963660800, 495586515116818125, 168827903320618878336, 21274128570193389587095, 1321109263548409835520000, 48378633136349277767794425, 1177042838234827583459440000},
%e A156173 {10180699028325, 3232089113385932800, 43304845277422684580625, 82435457461295106532780416, 42878835824239014254983869205, 8885253784030448738183147520000, 927610024989668734297857360967425, 57001313848230245122464621625840000, 2297271634742810443154153338805764581},
%e A156173 {10414855105976475, 95424198983606279987200, 15136126045591163828042953125, 201258420458750640859769304304896, 518543838148941095553869851505328175, 418310711031156574478261944188764160000, 142287668466497494704440569679875994730825, 24843911488189148287648216529610193612000000, 2552524038347870310755413660544832496799359491, 170310659060181679663863033233125976844488908800}
%t A156173 Clear[t, n, m, i, k];
%t A156173 t[n_, m_] = Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}];
%t A156173 Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}];
%t A156173 Flatten[%]
%t A156173 (* Second program: *)
%t A156173 T[n_, m_] := QFactorial[n, m + 1];
%t A156173 Table[T[n, m], {n, 1, 7}, {m, 1, n}] // Flatten (* _Jean-François Alcover_, Jan 18 2019 *)
%K A156173 nonn,tabl
%O A156173 1,2
%A A156173 _Roger L. Bagula_ and _Gary W. Adamson_, Feb 05 2009