

A158208


Triangle read by rows: p(x,n) = 2 if n = 0, Sum_{i=0..floor((n1)/2)} binomial(n, i)*(x  1)^i + x^n*Sum_{i=0..floor((n1)/2)} binomial(n, i)*(1/x  1)^i otherwise.


0



2, 1, 1, 1, 0, 1, 2, 3, 3, 2, 3, 4, 0, 4, 3, 6, 15, 10, 10, 15, 6, 10, 24, 15, 0, 15, 24, 10, 20, 70, 84, 35, 35, 84, 70, 20, 35, 120, 140, 56, 0, 56, 140, 120, 35, 70, 315, 540, 420, 126, 126, 420, 540, 315, 70, 126, 560, 945, 720, 210, 0, 210
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OFFSET

0,1


COMMENTS

The first half of every second row gives the coefficients of a polynomial approximation of f(0) = f'(0) = f'(1) = f''(0) = f''(1) = ... = 0 and f(1)=1: x, 2x^3 + 3x^2, 6x^5  15x^4 + 10x^3, ...  Martin Clever, Sep 12 2022


LINKS

Table of n, a(n) for n=0..61.


EXAMPLE

Triangle begins:
2;
1, 1;
1, 0, 1;
2, 3, 3, 2;
3, 4, 0, 4, 3;
6, 15, 10, 10, 15, 6;
10, 24, 15, 0, 15, 24, 10;
20, 70, 84, 35, 35, 84, 70, 20;
35, 120, 140, 56, 0, 56, 140, 120, 35;
70, 315, 540, 420, 126, 126, 420, 540, 315, 70;
126, 560, 945, 720, 210, 0, 210, 720, 945, 560, 126;
...


MATHEMATICA

p[x_, n_] = If[ n == 0, 2, Sum[Binomial[ n, i]*(x  1)^i, {i, 0, Floor[(n  1)/2]}] + Expand[x^n*Sum[Binomial[n, i]*(1/x  1)^ i, {i, 0, Floor[(n  1)/2]}]]];
Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[%]


CROSSREFS

Sequence in context: A035212 A318133 A068029 * A348652 A117274 A221650
Adjacent sequences: A158205 A158206 A158207 * A158209 A158210 A158211


KEYWORD

sign,tabl,uned,less


AUTHOR

Roger L. Bagula, Mar 13 2009


STATUS

approved



