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Search: id:A060338
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| A060338 |
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Triangle T(n,k) of coefficients of Meixner polynomials of degree n, k=0..n. |
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+0
4
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| 1, 1, 0, 1, 0, 1, 1, 0, 5, 0, 1, 0, 14, 0, 9, 1, 0, 30, 0, 89, 0, 1, 0, 55, 0, 439, 0, 225, 1, 0, 91, 0, 1519, 0, 3429, 0, 1, 0, 140, 0, 4214, 0, 24940, 0, 11025, 1, 0, 204, 0, 10038, 0, 122156, 0, 230481, 0, 1, 0, 285, 0, 21378, 0, 463490, 0, 2250621, 0, 893025
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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The Meixner polynomials M_n(x) satisfy the recurrence: M_(k+1)=x*M_k-k^2*M_(k-1), M_-1=0, M_0=1.
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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FORMULA
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E.g.f. : exp(x*arctan(y))/sqrt(1+y^2).
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EXAMPLE
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[1], [1, 0], [1, 0, -1], [1, 0, -5, 0], [1, 0, -14, 0, 9], [1, 0, -30, 0, 89, 0], [1, 0, -55, 0, 439, 0, -225], [1, 0, -91, 0, 1519, 0, -3429, 0], [1, 0, -140, 0, 4214, 0, -24940, 0, 11025], [1, 0, -204, 0, 10038, 0, -122156, 0, 230481, 0], ...
M_1(x)=x, M_2(x)=x^2-1, M_3(x)=x^3-5*x, M_4(x)=x^4-14*x^2+9, M_5(x)=x^5-30*x^3+89*x, M_6(x)=x^6-55*x^4+439*x^2-225,...
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CROSSREFS
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Cf. A028353.
Triangle without zeros: A094368.
Sequence in context: A082512 A068385 A071086 this_sequence A132795 A085198 A058064
Adjacent sequences: A060335 A060336 A060337 this_sequence A060339 A060340 A060341
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 30 2001
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