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A357737
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Expansion of e.g.f. sin( sqrt(3) * (exp(x) - 1) )/sqrt(3).
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2
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0, 1, 1, -2, -17, -65, -134, 331, 5797, 41092, 199621, 500731, -2996432, -58995155, -573624323, -4065029714, -19194210269, 7657775035, 1581081323122, 24363365708815, 260409006907921, 2127851409822892, 11143555796154673, -27234657667343081
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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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a(n) = Sum_{k=0..floor((n-1)/2)} (-3)^(k) * Stirling2(n,2*k+1).
a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A357726(k).
a(n) = ( Bell_n(sqrt(3) * i) - Bell_n(-sqrt(3) * i) )/(2 * sqrt(3) * i), where Bell_n(x) is n-th Bell polynomial and i is the imaginary unit.
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PROG
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(PARI) my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sin(sqrt(3)*(exp(x)-1))/sqrt(3)))))
(PARI) a(n) = sum(k=0, (n-1)\2, (-3)^k*stirling(n, 2*k+1, 2));
(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
a(n) = round((Bell_poly(n, sqrt(3)*I)-Bell_poly(n, -sqrt(3)*I))/(2*sqrt(3)*I));
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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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