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A357599
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Expansion of e.g.f. sinh(2 * log(1+x)) / 2.
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1
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0, 1, -1, 6, -30, 180, -1260, 10080, -90720, 907200, -9979200, 119750400, -1556755200, 21794572800, -326918592000, 5230697472000, -88921857024000, 1600593426432000, -30411275102208000, 608225502044160000, -12772735542927360000, 281000181944401920000
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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)} 4^k * Stirling1(n,2*k+1).
a(n) = (-1)^(n+1) * (n+1)!/4 for n > 2.
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PROG
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(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh(2*log(1+x))/2)))
(PARI) a(n) = sum(k=0, (n-1)\2, 4^k*stirling(n, 2*k+1, 1));
(PARI) a(n) = if(n<3, 0^n-(-1)^n, (-1)^(n+1)*(n+1)!/4);
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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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