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A270250 Triangle read by rows: coefficients of the polynomial (Sum_{i=0..k} (Product_{j=0..i} (x+j)))/(x*(x+2)).

%I A270250 #8 Oct 13 2017 21:39:48
%S A270250 1,2,1,5,5,1,17,24,9,1,77,131,68,14,1,437,833,529,151,20,1,2957,6107,
%T A270250 4458,1571,290,27,1,23117,50819,41164,16860,3870,505,35,1,204557,
%U A270250 473387,416230,191167,51379,8387,819,44,1,2018957,4880507,4589458,2309303,700776,134716,16541,1258,54,1
%N A270250 Triangle read by rows: coefficients of the polynomial (Sum_{i=0..k} (Product_{j=0..i} (x+j)))/(x*(x+2)).
%C A270250 The lines offset is 1, but the columns offset is 0.
%H A270250 Lajos Hajdu, Shanta Laishram, Szabolcs Tengely, <a href="http://dx.doi.org/10.4064/aa8271-10-2015">Power values of sums of products of consecutive integers</a>, Acta Arithmetica 172 (2016), 333-349.
%e A270250 First rows of this triangle:
%e A270250    1;
%e A270250    2,   1;
%e A270250    5,   5,   1;
%e A270250   17,  24,   9,   1;
%e A270250   77, 131,  68,  14,   1;
%e A270250   ...
%o A270250 (PARI) row(n) = Vecrev(sum(i=0, n, prod(j=0, i, x+j))/(x*(x+2)));
%Y A270250 Cf. A007489 (values of polynomial when x=2), A014288 (first column).
%K A270250 nonn,tabl
%O A270250 1,2
%A A270250 _Michel Marcus_, Mar 14 2016