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A200380
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Expansion of e.g.f. exp(x+x^2-1/6*x^3).
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0
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1, 1, 3, 6, 21, 51, 201, 498, 2241, 4581, 26991, 17766, 359613, -995409, 6968781, -53627454, 259953921, -2292378327, 13839388731, -108459180954, 809434284741, -6158416812309, 50614251147153, -407335408369614, 3478999597913601, -30042633320442099, 266107969086122151
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n!*sum(k=0..n, sum(j=0..k, binomial(j,n-3*k+2*j)*(-1)^(j-k)*6^(j-k)*binomial(k,j))/k!).
D-finite with recurrence 2*a(n) -2*a(n-1) +4*(-n+1)*a(n-2) +(n-1)*(n-2)*a(n-3)=0. - Bruno Berselli, Nov 17 2011
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PROG
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(Maxima) a(n):=n!*sum(sum(binomial(j, n-3*k+2*j)*(-1)^(j-k)*6^(j-k)*binomial(k, j), j, 0, k)/k!, k, 0, n);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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