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%I #13 Apr 08 2021 05:34:23
%S 4,20,20,72,224,72,232,1672,1672,232,716,10528,23528,10528,716,2172,
%T 60636,259688,259688,60636,2172,6544,331584,2485232,4674944,2485232,
%U 331584,6544,19664,1756304,21707888,69413168,69413168,21707888,1756304
%N Coefficients of Pascal's triangle polynomial minus MacMahon polynomial A060187 with a power of x divided out: q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x.
%C First elements in each row are: 3^n - 2*n - 1 (A061981).
%F q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x; t(n,m)=Coefficients(p(x,n)) with n starting at 2.
%e Triangle starts:
%e {4},
%e {20, 20},
%e {72, 224, 72},
%e {232, 1672, 1672, 232},
%e {716, 10528, 23528, 10528, 716},
%e {2172, 60636, 259688, 259688, 60636, 2172},
%e {6544, 331584, 2485232, 4674944, 2485232, 331584, 6544},
%e {19664, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304, 19664},
%e {59028, 9116096, 178300784, 906923072, 1527092216, 906923072, 178300784, 9116096, 59028}
%t q[x_, n_] = 2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p[x_, n_] = (q[x, n] - (x + 1)^n)/x; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 2, 10}]; Flatten[%]
%Y Cf. A061981, A060187.
%K nonn,tabl,uned,less
%O 2,1
%A _Roger L. Bagula_, Nov 01 2008
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