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A304209
Triangle read by rows: T(0,0)=1; T(n,k) = 2*T(n-1,k)-2*T(n-1,k-1)+T(n-1,k-2), for k = 0, 1, ..., 2*n; T(n,k)=0 for n or k < 0.
3
1, 2, -2, 1, 4, -8, 8, -4, 1, 8, -24, 36, -32, 18, -6, 1, 16, -64, 128, -160, 136, -80, 32, -8, 1, 32, -160, 400, -640, 720, -592, 360, -160, 50, -10, 1, 64, -384, 1152, -2240, 3120, -3264, 2624, -1632, 780, -280, 72, -12, 1, 128, -896, 3136, -7168, 11872, -15008, 14896, -11776, 7448, -3752, 1484, -448, 98, -14, 1
OFFSET
0,2
COMMENTS
Row n gives coefficients in expansion of (2-2*x+x^2)^n.
REFERENCES
Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3, pp. 178, 182.
EXAMPLE
Triangle begins:
1;
2, -2, 1;
4, -8, 8, -4, 1;
8, -24, 36, -32, 18, -6, 1;
16, -64, 128, -160, 136, -80, 32, -8, 1;
32, -160, 400, -640, 720, -592, 360, -160, 50, -10, 1;
64, -384, 1152, -2240, 3120, -3264, 2624, -1632, 780, -280, 72, -12, 1;
...
PROG
(PARI) T(n, k) = if ((n<0) || (k<0), 0, if ((n==0) && (k==0), 1, 2*T(n-1, k)-2*T(n-1, k-1)+T(n-1, k-2)));
tabf(nn) = for (n=0, nn, for (k=0, 2*n, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 10 2018
CROSSREFS
Row sums give A000012.
Sequence in context: A371889 A167622 A084606 * A137399 A158985 A295687
KEYWORD
tabf,easy,sign
AUTHOR
Shara Lalo, May 08 2018
STATUS
approved