A307996 - OEIS

%I #5 May 09 2019 15:00:21

%S 1,1,4,15,73,410,2591,18165,139266,1155509,10293729,97815520,

%T 986113613,10499247005,117603042220,1381191356979,16958788930317,

%U 217132031279842,2892337840164051,40002168264724193,573363461815952802,8502905138072937073,130268705062115090965,2058969680487762098496

%N Expansion of e.g.f. exp(1 - exp(x)*(1 - 2*x)).

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

%t nmax = 23; CoefficientList[Series[Exp[1 - Exp[x] (1 - 2 x)], {x, 0, nmax}], x] Range[0, nmax]!

%t a[n_] := a[n] = Sum[(2 k - 1) Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

%Y Cf. A000248, A000354, A003727, A005408, A275707.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, May 09 2019