A375953 - OEIS

%I #8 Sep 03 2024 12:14:31

%S 1,5,40,430,5770,92590,1726940,36682200,873793620,23061929940,

%T 667868085360,21052931727240,717531427466280,26289935772108120,

%U 1030422613932910800,43018144091244322560,1905711682795871222160,89284805444478025826640

%N Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^(5/2).

%F a(n) = (1/3) * Sum_{k=0..n} A001147(k+2) * |Stirling1(n,k)|.

%t nmax=17; CoefficientList[Series[1 / (1 + 2 * Log[1 - x])^(5/2),{x,0,nmax}],x]*Range[0,nmax]! (* _Stefano Spezia_, Sep 03 2024 *)

%o (PARI) a001147(n) = prod(k=0, n-1, 2*k+1);

%o a(n) = sum(k=0, n, a001147(k+2)*abs(stirling(n, k, 1)))/3;

%Y Cf. A088500, A367474, A367475, A375945.

%Y Cf. A001147.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 03 2024