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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}] 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,...}. LINKS 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)) EXAMPLE {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} 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[%] CROSSREFS Cf. A176697 Sequence in context: A104379 A142714 A276012 * A107415 A079174 A204137 Adjacent sequences:  A176698 A176699 A176700 * A176702 A176703 A176704 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 24 2010 STATUS approved

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Last modified October 22 12:47 EDT 2019. Contains 328318 sequences. (Running on oeis4.)