A367423 - OEIS

%I #7 Nov 18 2023 08:36:22

%S 1,1,5,41,465,6729,118437,2455809,58630401,1584058161,47783202213,

%T 1591924168185,58055219617425,2300356943749305,98409722434170885,

%U 4520749198158270225,221954573405993807745,11598560660172502840545,642753897983638032821445

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

%F a(n) = Sum_{k=0..n} 2^(n-k) * (Product_{j=0..k-1} (2*j+1)) * |Stirling1(n,k)|.

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

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

%Y Cf. A097397, A352117.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 18 2023