A370877 - OEIS

%I #9 Mar 04 2024 11:53:22

%S 1,1,3,15,111,1095,13605,204225,3597825,72788625,1663323795,

%T 42373980495,1190822561775,36596898673335,1221033470181525,

%U 43954996792932225,1698138394110583425,70082689941923083425,3077205709746516423075,143235112906380591471375

%N Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^2/2)) ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^2/2)))/x))

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

%Y Cf. A352410, A370878.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 03 2024