A372623 - OEIS

%I #8 May 08 2024 08:52:20

%S 1,1,3,11,48,247,1448,9445,67651,526704,4418875,39670270,378931567,

%T 3832882393,40886570975,458341921775,5382862509572,66050096110691,

%U 844741961321026,11236481306649167,155150031880549077,2219877203279634396,32860282502526114729

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

%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A000124(k-1) * a(n-k).

%t nmax = 22; CoefficientList[Series[Exp[Exp[x] (1 + x^2/2) - 1], {x, 0, nmax}], x] Range[0, nmax]!

%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (k (k - 1)/2 + 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]

%Y Cf. A000124, A209801, A279361.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, May 07 2024