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A052697
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Expansion of e.g.f. 1/(1-x^3-x^4).
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1
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1, 0, 0, 6, 24, 0, 720, 10080, 40320, 362880, 10886400, 119750400, 958003200, 24908083200, 523069747200, 6538371840000, 125536739328000, 3556874280960000, 70426110763008000, 1338096104497152000
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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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E.g.f.: 1/(1 - x^3 - x^4).
D-finite recurrence: a(0)=1, a(1)=0, a(2)=0, a(3)=6, a(n+4) = (24 + 26*n + 9*n^2 + n^3)*a(n+1) + (24 + 50*n + 35*n^2 + 10*n^3 + n^4)*a(n).
a(n) = (n!/283) * Sum_{alpha=RootOf(-1 + Z^3 + Z^4)} (- 16 - 73*alpha + 3*alpha^2 + 12*alpha^3)*alpha^(-1-n).
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MAPLE
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spec := [S, {S=Sequence(Prod(Z, Z, Union(Z, Prod(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[1/(1-x^3-x^4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 06 2016 *)
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PROG
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(Magma) [Factorial(n)*(&+[Binomial(k, n-3*k): k in [0..Floor(n/3)]]): n in [0..30]]; // G. C. Greubel, May 31 2022
(SageMath) [factorial(n)*sum(binomial(k, n-3*k) for k in (0..n//3)) for n in (0..30)] # G. C. Greubel, May 31 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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