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A159834
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Coefficient array of Hermite_H(n, (x-1)/sqrt(2))/(sqrt(2))^n.
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0
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1, -1, 1, 0, -2, 1, 2, 0, -3, 1, -2, 8, 0, -4, 1, -6, -10, 20, 0, -5, 1, 16, -36, -30, 40, 0, -6, 1, 20, 112, -126, -70, 70, 0, -7, 1, -132, 160, 448, -336, -140, 112, 0, -8, 1, -28, -1188, 720, 1344, -756, -252, 168, 0, -9, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Exponential Riordan array [exp(-x-x^2/2),x]. Inverse of A111062. Equal to A066325*(A007318)^{-1}.
First column is A001464. Row sums are (-1)^n*A001147 aerated.
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FORMULA
| G.f.: 1/(1-xy+x+x^2/(1-xy+x+2x^2/(1-xy+x+3x^2/(1-xy+x+4x^2/(1-... (continued fraction).
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EXAMPLE
| Triangle begins
1,
-1, 1,
0, -2, 1,
2, 0, -3, 1,
-2, 8, 0, -4, 1,
-6, -10, 20, 0, -5, 1,
16, -36, -30, 40, 0, -6, 1,
20, 112, -126, -70, 70, 0, -7, 1,
-132, 160, 448, -336, -140, 112, 0, -8, 1
Production matrix is
-1, 1,
-1, -1, 1,
0, -2, -1, 1,
0, 0, -3, -1, 1,
0, 0, 0, -4, -1, 1,
0, 0, 0, 0, -5, -1, 1,
0, 0, 0, 0, 0, -6, -1, 1,
0, 0, 0, 0, 0, 0, -7, -1, 1
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CROSSREFS
| Sequence in context: A127969 A081733 A102587 * A177995 A147786 A119387
Adjacent sequences: A159831 A159832 A159833 * A159835 A159836 A159837
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 23 2009
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