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A098494
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Triangle read by rows: coefficients of polynomials E(n,x) related to partitions with parts occurring at most thrice.
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2
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1, 1, -1, 1, -5, 4, 1, -12, 35, -30, 1, -22, 143, -362, 312, 1, -35, 405, -2065, 4814, -4200, 1, -51, 925, -7965, 35434, -78744, 69120, 1, -70, 1834, -24010, 173929, -709240, 1525236, -1345680, 1, -92, 3290, -61040, 655529, -4235588, 16255420
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| The polynomials generate (-1)^k*n! times the diagonals of A098493.
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REFERENCES
| A. Fink, R. K. Guy and M. Krusemeyer, Partitions with parts occurring at most thrice, in preparation.
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EXAMPLE
| E(0,x) = 1
E(1,x) = x - 1
E(2,x) = x^2 - 5*x + 4
E(3,x) = x^3 - 12*x^2 + 35*x - 30
E(4,x) = x^4 - 22*x^3 + 143*x^2 - 362*x + 312
E(5,x) = x^5 - 35*x^4 + 405*x^3 - 2065*x^2 + 4814*x - 4200
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CROSSREFS
| Columns include -A000326. Constant terms E(n, 0) = -E(n-1, -1) = n!/2*A085455 = (-1)^n*n!*A005773. Row sums are E(n, 1) = (-1)^n*n!*A005774.
Sequence in context: A072222 A197001 A005752 * A008955 A182824 A152862
Adjacent sequences: A098491 A098492 A098493 * A098495 A098496 A098497
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KEYWORD
| sign,tabl
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2004
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