cp's OEIS Frontend

A162499 Triangle read by rows in which row n gives coefficients of the expansion of the polynomial Product( (1-x^(3*k))/(1-x), k=1..n).

%I A162499 #22 Jul 08 2018 11:13:14
%S A162499 1,1,1,1,1,2,3,3,3,3,2,1,1,3,6,9,12,15,17,18,18,17,15,12,9,6,3,1,1,4,
%T A162499 10,19,31,46,63,81,99,116,131,143,151,154,151,143,131,116,99,81,63,46,
%U A162499 31,19,10,4,1,1,5,15,34,65,111,174,255,354,470,601,744,895
%N A162499 Triangle read by rows in which row n gives coefficients of the expansion of the polynomial Product( (1-x^(3*k))/(1-x), k=1..n).
%D A162499 A. V. Yurkin, New binomial and new view on light theory, (book), 2013, 78 pages, no publisher listed.
%H A162499 G. C. Greubel, <a href="/A162499/b162499.txt">Rows n=0..20 of triangle, flattened</a>
%H A162499 A. V. Yurkin, <a href="http://www.mce.biophys.msu.ru/eng/archive/abstracts/mce19/sect1138/doc150220/">On similarity of systems of geometrical and arithmetic triangles</a>, in Mathematics, Computing, Education Conference XIX, 2012.
%H A162499 A. V. Yurkin, <a href="http://arxiv.org/abs/1302.6287">New view on the diffraction discovered by Grimaldi and Gaussian beams</a>, arXiv:1302.6287 [physics.optics], 2013.
%e A162499 Triangle begins:
%e A162499 1
%e A162499 1, 1, 1
%e A162499 1, 2, 3, 3, 3, 3, 2, 1,
%e A162499 1, 3, 6, 9, 12, 15, 17, 18, 18, 17, 15, 12, 9, 6, 3, 1,
%e A162499 1, 4, 10, 19, 31, 46, 63, 81, 99, 116, 131, 143, 151, 154, 151, 143, 131, 116, 99, 81, 63, 46, 31, 19, 10, 4, 1
%e A162499 1, 5, 15, 34, 65, 111, 174, 255, 354, 470, 601, 744, 895, 1049, 1200, 1342, 1469, 1575, 1655, 1705, 1722, 1705, 1655, 1575, 1469, 1342, 1200, 1049, 895, 744, 601, 470, 354, 255, 174, 111, 65, 34, 15, 5, 1,
%e A162499 ...
%t A162499 row[n_] := CoefficientList[Product[(1 - x^(3*k))/(1 - x), {k, 1, n}], x]; Table[row[n], {n, 0, 5}] // Flatten (* _Jean-François Alcover_, Sep 19 2016 *)
%Y A162499 Rows give A162500, ...
%K A162499 nonn,tabf,look
%O A162499 0,6
%A A162499 _N. J. A. Sloane_, Dec 02 2009