A357599 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

Offset: 0

Author

Seiichi Manyama, Oct 05 2022

Keywords

• sign

Crossrefs

Cf. A001710, A133799, A357598.

Programs

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);

Formula

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.