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A357739
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a(n) = Sum_{k=0..floor((n-1)/2)} (-n)^k * Stirling2(n,2*k+1).
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0
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0, 1, 1, -2, -23, -99, 1, 4411, 45137, 205570, -1270799, -38876573, -441073511, -1921300835, 34908578433, 994442615986, 13032718992033, 59450652771077, -1794250960044623, -57608157168424497, -901446808420344919, -5274602459214885362, 160827105304127790529
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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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For n > 0, a(n) = n! * [x^n] sin( sqrt(n) * (exp(x) - 1) )/sqrt(n).
For n > 0, a(n) = ( Bell_n(sqrt(n) * i) - Bell_n(-sqrt(n) * i) )/(2 * sqrt(n) * 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) a(n) = sum(k=0, (n-1)\2, (-n)^k*stirling(n, 2*k+1, 2));
(PARI) a(n) = if(n==0, 0, round(n!*polcoef(sin(sqrt(n)*(exp(x+x*O(x^n))-1))/sqrt(n), n)));
(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
a(n) = if(n==0, 0, round((Bell_poly(n, sqrt(n)*I)-Bell_poly(n, -sqrt(n)*I))/(2*sqrt(n)*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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