A370992 - OEIS

%I #12 Mar 07 2024 01:32:12

%S 1,0,0,0,4,10,20,35,5656,55524,352920,1801965,85636540,1762160686,

%T 22992890284,232001269955,6581012518640,197506018950920,

%U 4224661065644016,69931313468126169,1757395269147356340,60785516594782517650,1818493252905482003620

%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3/6*(exp(x) - 1)) ).

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (n+k)! * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^3/6*(exp(x)-1)))/x))

%o (PARI) a(n) = sum(k=0, n\4, (n+k)!*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!))/(n+1);

%Y Cf. A370988, A370991.

%Y Cf. A353999.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Mar 06 2024