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Search: id:A098503
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| A098503 |
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Triangle T(n,k) by rows: coefficients of 2^n * L(n,1/2,x), with L the generalized Laguerre polynomials. |
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+0
4
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| 1, -2, 3, 4, -20, 15, -8, 84, -210, 105, 16, -288, 1512, -2520, 945, -32, 880, -7920, 27720, -34650, 10395, 64, -2496, 34320, -205920, 540540, -540540, 135135, -128, 6720, -131040, 1201200, -5405400, 11351340, -9459450, 2027025, 256, -17408
(list; table; graph; listen)
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OFFSET
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0,2
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FORMULA
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T(n, k) = (-2)^n * n!/k! * C(n+1/2, n-k), n>=0, k<=n.
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EXAMPLE
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2^0 L(0,1/2,x) = 1.
2^1 L(1,1/2,x) = -2*x + 3.
2^2 L(2,1/2,x) = 4*x^2 - 20*x + 15.
2^3 L(3,1/2,x) = -8*x^3 + 84*x^2 - 210*x + 105.
2^4 L(4,1/2,x) = 16*x^4 - 288*x^3 + 1512*x^2 - 2520*x + 945.
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CROSSREFS
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Columns include (-1)^n times A000079, n/2*A014480. Diagonals include A001147, -A000906, 4*A001881.
Adjacent sequences: A098500 A098501 A098502 this_sequence A098504 A098505 A098506
Sequence in context: A058772 A012285 A012281 this_sequence A092974 A058186 A024632
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KEYWORD
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sign,tabl
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 15 2004
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