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}].
1, 1, 1, 1, -2, 3, 1, 12, -18, 7, 1, -108, 202, -113, 20, 1, 1404, -2948, 2092, -610, 63, 1, -23556, 54044, -44708, 17070, -3057, 208, 1, 488364, -1200160, 1109956, -505515, 121368, -14723, 711, 1, -12091476, 31417568, -31667516, 16389909, -4770792
Offset: 0
Examples
{1},
{1, 1},
{1, -2, 3},
{1, 12, -18, 7},
{1, -108, 202, -113, 20},
{1, 1404, -2948, 2092, -610, 63},
{1, -23556, 54044, -44708, 17070, -3057, 208},
{1, 488364, -1200160, 1109956, -505515, 121368, -14723, 711},
{ 1, -12091476, 31417568, -31667516, 16389909, -4770792, 788989, -69177, 2496},
{1, 348530604, -948701728, 1024833540, -585398187, 196013064, -39780995, 4814247, -319488, 8944},
{1, -11473374036, 32495091200, -37179387060, 22990648853, -8578056786, 2021526799, -303047853, 28023372, -1457066, 32578}
Crossrefs
Cf. A176697
Programs
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Mathematica
a[0] := 1; a[1] := 1;a[2]=3 a[n_] := a[n] = Table[a[i], {i, 0, n - 1}].Table[a[n - 1 - i], {i, 0, n - 1}]; p[x_, n_] := Sum[a[m]*m!*Binomial[x, m], {m, 0, n}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
Formula
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}];
t(n,m)=coefficients(p(x,n))
Comments