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A158785
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Expansion of e.g.f.: exp(t*x)/(1 - x^2/t - t^3*x^3).
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1
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1, 0, 1, 2, 0, 0, 1, 0, 6, 0, 0, 7, 24, 0, 0, 12, 0, 0, 25, 0, 120, 0, 0, 260, 0, 0, 61, 720, 0, 0, 360, 0, 0, 1470, 0, 0, 841, 0, 5040, 0, 0, 15960, 0, 0, 5082, 0, 0, 5251, 40320, 0, 0, 20160, 0, 0, 122640, 0, 0, 134456, 0, 0, 20497, 0, 362880, 0, 0, 1512000
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OFFSET
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0,4
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LINKS
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FORMULA
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T(n, k) = coefficients of e.g.f.: t^floor(n/2)*exp(t*x)/(1 - x^2/t - t^3*x^3).
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EXAMPLE
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Irregular triangle begins as:
1;
0, 1;
2, 0, 0, 1;
0, 6, 0, 0, 7;
24, 0, 0, 12, 0, 0, 25;
0, 120, 0, 0, 260, 0, 0, 61;
720, 0, 0, 360, 0, 0, 1470, 0, 0, 841;
0, 5040, 0, 0, 15960, 0, 0, 5082, 0, 0, 5251;
40320, 0, 0, 20160, 0, 0, 122640, 0, 0, 134456, 0, 0, 20497;
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MATHEMATICA
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Table[CoefficientList[Expand[t^Floor[n/2]*n!*SeriesCoefficient[Series[Exp[t*x]/(1 - x^2/t - t^3*x^3), {x, 0, 20}], n]], t], {n, 0, 10}]//Flatten
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PROG
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(Sage)
f(x, t) = exp(t*x)/(1 - x^2/t - t^3*x^3)
def A158785(n, k): return ( factorial(n)*t^(n//2)*( f(x, t) ).series(x, 20).list()[n] ).series(t, 2*n+1).list()[k]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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