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Erroneous version of A103450.
2

%I #27 Feb 15 2014 20:22:36

%S 1,1,1,1,3,1,1,5,5,1,1,7,12,7,1,1,9,22,22,9,1,1,11,35,50,35,11,11,13,

%T 51,95,95,51,13,1,1,15,70,161,210,161,70,15,1,1,17,92,252,406,406,252,

%U 92,17,1

%N Erroneous version of A103450.

%C The triangle is bisymmetric, row sums = A045623: (1, 2, 5, 12, 28, 64,...). A114219(signed) * A007318 = A128255.

%F A007318 * A114219, where the latter is signed: {1; 0,1; 0,1,1; 0,-1,2,1; 0,1,-2,3,1;...}. The signed version of A114219 = A097807 * A128229.

%F T(n,k) = k Binomial[n-2,k-1] + Binomial[n-2,k-2], for 1 <= k <= n. - O. D'Antona, Dec 17 2007

%e First few rows of the triangle are:

%e 1;

%e 1, 1;

%e 1, 3, 1;

%e 1, 5, 5, 1;

%e 1, 7, 12, 7, 1;

%e 1, 9, 22, 22, 9, 1;

%e 1, 11, 35, 50, 35, 11, 1;

%e ...

%e Central coefficients T(2n,n) = A141222. - _Emanuele Munarini_, Jun 01 2012

%o (Maxima) T(n,k):=k*binomial(n-2,k-1)+binomial(n-2,k-2);

%o create_list(T(n+1,k+1),n,0,30,k,0,n); [_Emanuele Munarini_, Jun 01 2012]

%Y Cf. A128229, A007318, A114219, A128255, A045623, A141222.

%K dead

%O 1,5

%A _Gary W. Adamson_, Feb 20 2007

%E Typo in sequence corrected by O. D'Antona (dantona(AT)dico.unimi.it), Dec 17 2007