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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.
(PARI) a(n) = if(n<3, 0^n-(-1)^n, (-1)^(n+1)*(n+1)!/4);
(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));
allocated for Seiichi Manyama
Expansion of e.g.f. sinh(2 * log(1+x)) / 2.
0, 1, -1, 6, -30, 180, -1260, 10080, -90720, 907200, -9979200, 119750400, -1556755200, 21794572800, -326918592000, 5230697472000, -88921857024000, 1600593426432000, -30411275102208000, 608225502044160000, -12772735542927360000, 281000181944401920000
0,4
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Seiichi Manyama, Oct 05 2022
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editing
allocated for Seiichi Manyama
allocated
approved