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 A130471 First differences of antidiagonal sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j. 3

%I #3 Sep 08 2022 08:45:30

%S 0,2,5,21,106,640,4527,36539,331508,3338358,36946489,445724977,

%T 5821580670,81839381996,1232102291651,19778348559015,337223021210632,

%U 6086161135368034,115915940643233613,2323409451689985053

%N First differences of antidiagonal sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.

%C a(n) = A130470(n+1) - A130470(n).

%e a(7) = A130470(8) - A130470(7) = 5302 - 775 = 4527.

%o (Magma) m:=21; T:=[ [ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]: j in [1..m] ]; S:=[ &+[ T[j-k+1][k]: k in [1..(j+1) div 2] ]: j in [1..m] ]; [ S[j+1]-S[j]: j in [1..m-1] ];

%Y Cf. A130469 (T read by rows), A129867 (row sums), A130470 (antidiagonal sums).

%K nonn

%O 1,2

%A _Klaus Brockhaus_, May 28 2007

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Last modified December 4 18:39 EST 2023. Contains 367563 sequences. (Running on oeis4.)