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A357599 Expansion of e.g.f. sinh(2 * log(1+x)) / 2. 1

%I #10 Oct 05 2022 12:35:36

%S 0,1,-1,6,-30,180,-1260,10080,-90720,907200,-9979200,119750400,

%T -1556755200,21794572800,-326918592000,5230697472000,-88921857024000,

%U 1600593426432000,-30411275102208000,608225502044160000,-12772735542927360000,281000181944401920000

%N Expansion of e.g.f. sinh(2 * log(1+x)) / 2.

%F a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * Stirling1(n,2*k+1).

%F a(n) = (-1)^(n+1) * (n+1)!/4 for n > 2.

%o (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh(2*log(1+x))/2)))

%o (PARI) a(n) = sum(k=0, (n-1)\2, 4^k*stirling(n, 2*k+1, 1));

%o (PARI) a(n) = if(n<3, 0^n-(-1)^n, (-1)^(n+1)*(n+1)!/4);

%Y Cf. A001710, A133799, A357598.

%K sign

%O 0,4

%A _Seiichi Manyama_, Oct 05 2022

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Last modified April 16 10:08 EDT 2024. Contains 371698 sequences. (Running on oeis4.)