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A287697 Triangle read by rows, (Sum_{k=0..n} T[n,k]*x^k) / (1-x)^(n+1) are generating functions of the columns of A287698.

%I A287697 #12 Jun 01 2017 12:03:49
%S A287697 1,0,1,0,1,7,0,1,52,163,0,1,341,4499,8983,0,1,2246,98256,660746,
%T A287697 966751,0,1,15177,2045282,35677082,155729277,179781181,0,1,104952,
%U A287697 42658239,1754605504,17446464519,55690144728,53090086057
%N A287697 Triangle read by rows, (Sum_{k=0..n} T[n,k]*x^k) / (1-x)^(n+1) are generating functions of the columns of A287698.
%F A287697 T(n,n) = A212856(n).
%F A287697 Sum_{k=0..n} T(n,k) = A000442(n).
%e A287697 Triangle starts:
%e A287697 0: [1]
%e A287697 1: [0, 1]
%e A287697 2: [0, 1,      7]
%e A287697 3: [0, 1,     52,      163]
%e A287697 4: [0, 1,    341,     4499,       8983]
%e A287697 5: [0, 1,   2246,    98256,     660746,      966751]
%e A287697 6: [0, 1,  15177,  2045282,   35677082,   155729277,   179781181]
%e A287697 7: [0, 1, 104952, 42658239, 1754605504, 17446464519, 55690144728, 53090086057]
%e A287697 ...
%e A287697 Let q4(x) = (x + 341*x^2 + 4499*x^3 + 8983*x^4) / (1-x)^5 then the coefficients of the series expansion of q4 are column 4 of A287698.
%p A287697 A287697_row := n -> Delta(A287696_poly(n), n): # Delta defined in A287315.
%p A287697 for n from 0 to 9 do A287697_row(n) od;
%p A287697 A287697_eulerian := (n,x) -> add(A287697_row(n)[k+1]*x^k,k=0..n)/(1-x)^(n+1):
%p A287697 for n from 0 to 4 do A287697_eulerian(n,x) od;
%Y A287697 Cf. A000442, A212856, A287696, A287698.
%K A287697 nonn,tabl
%O A287697 0,6
%A A287697 _Peter Luschny_, May 30 2017