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 A156141 Triangle T(n,k) = A008517(n,k+1)+A008517(n,n+1-k) read by rows. 3

%I

%S 2,1,1,1,4,1,1,14,14,1,1,46,116,46,1,1,172,772,772,172,1,1,834,5160,

%T 8800,5160,834,1,1,5280,39594,90260,90260,39594,5280,1,1,40814,361086,

%U 981104,1288040,981104,361086,40814,1,1,363884,3801180,12088796

%N Triangle T(n,k) = A008517(n,k+1)+A008517(n,n+1-k) read by rows.

%C Row sums are 2*A001147(n).

%H E. W. Weisstein, <a href="http://mathworld.wolfram.com/Second-OrderEulerianTriangle.html">Second-Order Eulerian Triangle</a>

%F T(n,0)=T(n,n) =1, n>=1.

%F T(n,k)= A008517(n,k+1)+A008517(n,n+1-k), n>1, 0<k<n.

%F T(n,k)= T(n,n-k) .

%e {2},

%e {1, 1},

%e {1, 4, 1},

%e {1, 14, 14, 1},

%e {1, 46, 116, 46, 1},

%e {1, 172, 772, 772, 172, 1},

%e {1, 834, 5160, 8800, 5160, 834, 1},

%e {1, 5280, 39594, 90260, 90260, 39594, 5280, 1},

%e {1, 40814, 361086, 981104, 1288040, 981104, 361086, 40814, 1},

%e {1, 363884, 3801180, 12088796, 18205564, 18205564, 12088796, 3801180, 363884, 1},

%e {1, 3630826, 44557888, 167513072, 283669904, 310714768, 283669904, 167513072, 44557888, 3630826, 1}

%t e[n_, 0] := 1;

%t e[n_, k_] := 0 /; k >= n;

%t e[n_, k_] := (k + 1)e[n - 1, k] + (2n - k - 1)e[n - 1, k - 1];

%t Table[Table[e[n, k] + e[n, n - k], {k, 0, n}], {n, 0, 10}];

%t Flatten[%]

%Y Cf. A008517

%K nonn,tabl

%O 0,1

%A _Roger L. Bagula_, Feb 04 2009

%E Definition simplified by the Associate Editors of the OEIS Sep 17 2009

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