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A124448
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Riordan array (sqrt(1+4x^2)-2x, (1+2x-sqrt(1+4x^2))/2).
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2
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1, -2, 1, 2, -3, 1, 0, 4, -4, 1, -2, -1, 7, -5, 1, 0, -4, -4, 11, -6, 1, 4, 2, -6, -10, 16, -7, 1, 0, 8, 8, -6, -20, 22, -8, 1, -10, -5, 11, 19, -1, -35, 29, -9, 1, 0, -20, -20, 7, 34, 13, -56, 37, -10, 1, 28, 14, -26, -46, -12, 49, 41, -84
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Inverse of triangle A106195.
Row sums are A105523 (expansion of 1-xc(-x^2) where c(x) is the g.f. of A000108).
Product of A007318 and A124448 is inverse of A053538.
A124448*A007318 = A106180, as infinite lower triangular matrices . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2007
Triangle T(n,k), read by rows, given by (-2,1,-1,1,-1,1,-1,1,-1,...) DELTA (1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938 . - From DELEHAM Philippe, Oct 09 2011.
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EXAMPLE
| Triangle begins
1,
-2, 1,
2, -3, 1,
0, 4, -4, 1,
-2, -1, 7, -5, 1,
0, -4, -4, 11, -6, 1,
4, 2, -6, -10, 16, -7, 1,
0, 8, 8, -6, -20, 22, -8, 1
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PROG
| (PARI)
N=12;
T(n, k)=sum(i=0, n-k, binomial(k, i)*binomial(n-k, i)*2^(n-k-i));
M=matrix(N, N);
for(n=1, N, for(k=1, n, M[n, k]=T(n-1, k-1))); /* A106195 */
A=M^-1; /* A124448 */
/* for (n=1, N, for(k=1, n, print1(M[n, k], ", "))); */ /* A106195 */
for (n=1, N, for(k=1, n, print1(A[n, k], ", "))); /* A124448 */
/* Joerg Arndt, May 14 2011 */
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CROSSREFS
| Cf. A106195, A000045, A164948, A164942
Sequence in context: A132815 A167684 A094646 * A143343 A138243 A131796
Adjacent sequences: A124445 A124446 A124447 * A124449 A124450 A124451
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 01 2006
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EXTENSIONS
| Edited by N. J. A. Sloane, Dec 29 2011
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