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A098277
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Coefficients of polynomials D(n,x) related to median Euler numbers.
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5
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1, 2, 2, 8, 20, 12, 48, 224, 344, 168, 384, 2880, 8096, 9872, 4272, 3840, 42240, 186816, 407936, 430688, 171168, 46080, 698880, 4451328, 15030528, 27944576, 26627648, 9915072, 645120, 12902400, 111605760, 535271424, 1519126272
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 2^n(x+1) divides D(n,x).
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LINKS
| A. Randrianarivony and J. Zeng, Une famille des polynomes qui interpole plusieurs suites..., Adv. Appl. Math. 17 (1996), 1-26.
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FORMULA
| Recurrence: D(0, x)=1, D(n, x) = (x+1)(x+2)D(n-1, x+2) - x(x+1)D(n-1, x).
G.f.: Sum[n>=0, D(n, x)t^n] = 1/(1-2(x+1)t/(1-2(x+2)t/(1-4(x+3)t/(1-4(x+4)t/...)))).
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EXAMPLE
| D(0,x) = 1,
D(1,x) = 2*x + 2,
D(2,x) = 8*x^2 + 20*x + 12,
D(3,x) = 48*x^3 + 224*x^2 + 344*x + 168,
D(4,x) = 384*x^4 + 2880*x^3 + 8096*x^2 + 9872*x + 4272.
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PROG
| (PARI) D(n, x)=if(n<1, 1, (x+1)*(x+2)*D(n-1, x+2)-x*(x+1)*D(n-1, x))
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CROSSREFS
| D(n, 1/2) = A002832(n+1), D(n, -1/2) = A000657(n).
D(n, 0)/2^n = A098278(n), D(n, 1)/2^n = A098279(n).
Leading coefficients are A000165. Constant terms are in A098431.
Sequence in context: A169888 A168506 A067640 * A080040 A060823 A178076
Adjacent sequences: A098274 A098275 A098276 * A098278 A098279 A098280
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KEYWORD
| nonn,tabl
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AUTHOR
| Ralf Stephan, Sep 07 2004
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