%I #4 Dec 05 2017 09:39:51

%S 1,2,2,3,12,4,4,36,48,8,5,80,240,160,16,6,150,800,1200,480,32,7,252,

%T 2100,5600,5040,1344,64,8,392,4704,19600,31360,18816,3584,128,9,576,

%U 9408,56448,141120,150528,64512,9216,256,10,810,17280,141120,508032

%N A triangle of polynomial coefficients related to Mittag-Leffler polynomials: p(x,n)=Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x).

%D Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 75-76

%F p(x,n)=Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x);

%F p(x,n)=n Hypergeometric2F1[1 - n, 1 - n, 2, 2 x];

%F t(n,m)=coefficiemts(p(x,n))

%F T(n,m) = 2^m*A103371(n,m). - _R. J. Mathar_, Dec 05 2017

%e 1;

%e 2, 2;

%e 3, 12, 4;

%e 4, 36, 48, 8;

%e 5, 80, 240, 160, 16;

%e 6, 150, 800, 1200, 480, 32;

%e 7, 252, 2100, 5600, 5040, 1344, 64;

%e 8, 392, 4704, 19600, 31360, 18816, 3584, 128;

%e 9, 576, 9408, 56448, 141120, 150528, 64512, 9216, 256;

%e 10, 810, 17280, 141120, 508032, 846720, 645120, 207360, 23040, 512;

%t Clear[t0, p, x, n, m];

%t p[x_, n_] = Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x);

%t Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}];

%t Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}];

%t Flatten[%]

%Y A142983, A142978, A047781 (row sums).

%K nonn,tabl,uned

%O 0,2

%A _Roger L. Bagula_, Feb 04 2009