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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

Table of n, a(n) for n=0..41.

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.)