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A104558
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Triangle, read by rows, equal to the matrix inverse of A104557 and related to Laguerre polynomials.
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1
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1, -1, 1, 0, -2, 1, 0, 2, -4, 1, 0, 0, 6, -6, 1, 0, 0, -6, 18, -9, 1, 0, 0, 0, -24, 36, -12, 1, 0, 0, 0, 24, -96, 72, -16, 1, 0, 0, 0, 0, 120, -240, 120, -20, 1, 0, 0, 0, 0, -120, 600, -600, 200, -25, 1, 0, 0, 0, 0, 0, -720, 1800, -1200, 300, -30, 1, 0, 0, 0, 0, 0, 720, -4320, 5400, -2400, 450, -36, 1, 0, 0, 0, 0, 0, 0, 5040, -15120
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Even-indexed rows are found in A066667 (generalized Laguerre polynomials). Odd-indexed rows are found in A021009 (Laguerre polynomials L_n(x)). Row sums equal A056920 (offset 1). Absolute row sums equal A056953 (offset 1).
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FORMULA
| T(n, k) = (-1)^(n-k)*(n-k)!*C(1+[n/2], k+1-[(n+1)/2])*C([(n+1)/2], k-[n/2]).
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EXAMPLE
| Rows begin:
1;
-1,1;
0,-2,1;
0,2,-4,1;
0,0,6,-6,1;
0,0,-6,18,-9,1;
0,0,0,-24,36,-12,1;
0,0,0,24,-96,72,-16,1;
0,0,0,0,120,-240,120,-20,1;
0,0,0,0,-120,600,-600,200,-25,1; ...
Unsigned columns read downwards equals rows of
matrix inverse A104557 read backwards:
1;
1,1;
2,2,1;
6,6,4,1;
24,24,18,6,1;
120,120,96,36,9,1; ...
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PROG
| (PARI) {T(n, k)=(-1)^(n-k)*(n-k)!*binomial(1+n\2, k+1-(n+1)\2)*binomial((n+1)\2, k-n\2)}
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CROSSREFS
| Cf. A104557, A066667, A021009, A056920, A056953.
Sequence in context: A110280 A061009 A144106 * A206022 A115247 A204163
Adjacent sequences: A104555 A104556 A104557 * A104559 A104560 A104561
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KEYWORD
| sign,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Mar 16 2005
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