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Triangle A060058 by diagonals.
7

%I #5 Mar 31 2012 13:20:05

%S 1,1,1,5,5,1,61,61,14,1,1385,1385,331,30,1,50521,50521,12284,1211,55,

%T 1,2702765,2702765,663061,68060,3486,91,1,199360981,199360981,

%U 49164554,5162421,281210,8526,140,1

%N Triangle A060058 by diagonals.

%C Row sums give A060059. Columns give A000364 (Euler numbers), A000364, A060075-78 for m=0,..,5.

%C Triangle can be used to express the Euler numbers E(n)=A000364(n), n >= 2, in terms of the numbers A060080 (scaled sums of squares), according to E(n+2)= sum(a(n,m)*A060080(m+2),m=0..n).

%F a(n, m)= a(n-1, m-1)+(m+1)^2*a(n, m+1), a(n, -1) := 0, a(0, 0)=1, a(n, m)=0 if n<m.

%F a(n, m)=A060058(n, n-m).

%e {1}; {1,1}; {5,5,1}; {61,61,14,1}; ...

%K nonn,easy,tabl

%O 0,4

%A _Wolfdieter Lang_, Mar 16 2001