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A176701 A polynomial coefficient triangle sequence:a(n)=vector(a(n-1)).Reverse(vector(a(n-1));a(0)=1;a(1)=1;a[2]=3;p(x,n)=Sum[a(m)*m!*Binomial[x, m], {m, 0, n}].

%I A176701 #4 Jul 22 2025 07:59:27
%S A176701 1,1,1,1,-2,3,1,12,-18,7,1,-108,202,-113,20,1,1404,-2948,2092,-610,63,
%T A176701 1,-23556,54044,-44708,17070,-3057,208,1,488364,-1200160,1109956,
%U A176701 -505515,121368,-14723,711,1,-12091476,31417568,-31667516,16389909,-4770792
%N A176701 A polynomial coefficient triangle sequence:a(n)=vector(a(n-1)).Reverse(vector(a(n-1));a(0)=1;a(1)=1;a[2]=3;p(x,n)=Sum[a(m)*m!*Binomial[x, m], {m, 0, n}].
%C A176701 Row sums are:
%C A176701 {1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,...}.
%F A176701 a(n)=vector(a(n-1)).Reverse(vector(a(n-1));
%F A176701 a(0)=1;a(1)=1;a[2]=3;
%F A176701 p(x,n)=Sum[a(m)*m!*Binomial[x, m], {m, 0, n}];
%F A176701 t(n,m)=coefficients(p(x,n))
%e A176701 {1},
%e A176701 {1, 1},
%e A176701 {1, -2, 3},
%e A176701 {1, 12, -18, 7},
%e A176701 {1, -108, 202, -113, 20},
%e A176701 {1, 1404, -2948, 2092, -610, 63},
%e A176701 {1, -23556, 54044, -44708, 17070, -3057, 208},
%e A176701 {1, 488364, -1200160, 1109956, -505515, 121368, -14723, 711},
%e A176701 { 1, -12091476, 31417568, -31667516, 16389909, -4770792, 788989, -69177, 2496},
%e A176701 {1, 348530604, -948701728, 1024833540, -585398187, 196013064, -39780995, 4814247, -319488, 8944},
%e A176701 {1, -11473374036, 32495091200, -37179387060, 22990648853, -8578056786, 2021526799, -303047853, 28023372, -1457066, 32578}
%t A176701 a[0] := 1; a[1] := 1;a[2]=3
%t A176701 a[n_] := a[n] = Table[a[i], {i, 0, n - 1}].Table[a[n - 1 - i], {i, 0, n - 1}];
%t A176701 p[x_, n_] := Sum[a[m]*m!*Binomial[x, m], {m, 0, n}];
%t A176701 Table[CoefficientList[p[x, n], x], {n, 0, 10}];
%t A176701 Flatten[%]
%Y A176701 Cf. A176697
%K A176701 sign,tabl,uned
%O A176701 0,5
%A A176701 _Roger L. Bagula_, Apr 24 2010