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A108032 Triangle T(n,k), 0<=k<=n, read by rows, defined by : T(0,0) = 1, T((n,k) = 0 if n<k or if k<0, T(n,k) = k*T(n-1, k-1) + (2n-2k-1)*T(n-1, k). 0

%I

%S 1,1,1,3,2,2,15,9,6,6,105,60,36,24,24,945,525,300,180,120,120,10395,

%T 5670,3150,1800,1080,720,720,135135,72765,39690,22050,12600,7560,5040,

%U 5040,2027025,1081080,582120,317520,176400,100800,60480,40320,40320

%N Triangle T(n,k), 0<=k<=n, read by rows, defined by : T(0,0) = 1, T((n,k) = 0 if n<k or if k<0, T(n,k) = k*T(n-1, k-1) + (2n-2k-1)*T(n-1, k).

%F Sum{ k, 0<=k<=n} T(n, k) = A034430(n).

%F T(n, k) = A001147(n-k)*k!*binomial(n, k).

%F E.g.f.: 1/(1-t*x)*1/sqrt(1-2*x) = 1 + x*(1+t) + x^2/2!*(3+2*t+2*t^2) + .... - _Peter Bala_, Jun 27 2012

%e 1;

%e 1, 1;

%e 3, 2, 2;

%e 15, 9, 6, 6;

%e 105, 60, 36, 24, 24; ...

%Y Diagonals : A001147, A001193, A000142.

%Y Cf. A034430 (row sums).

%K nonn,easy,tabl

%O 0,4

%A _Philippe Deléham_, Jun 01 2005

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)