A396965 - OEIS

%I #33 Jul 17 2026 01:07:39

%S 1,1,2,18,216,4360,125040,4757424,233179520,14258991744,1060121721600,

%T 94009965280000,9789344262601728,1181209592291349504,

%U 163306868988824078336,25621879112031299758080,4524060645635205169643520,892453349895680565864595456,195425578879660458241000538112

%N E.g.f. A(x) satisfies A(x) = 1 + x * A(x * exp(2*x)).

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

%F a(0) = 1; a(n) = n * A397882(n-1).

%F E.g.f.: 1 + x*B(x), where B(x) is the e.g.f. of A397882.

%e A(x)         = 1 + x + x^2 + 3*x^3 + 9*x^4 + 109/3*x^5 + 521/3*x^6 + ...

%e A(x * exp(2*x)) =  1 + x   + 3*x^2 + 9*x^3 + 109/3*x^4 + 521/3*x^5 + ...

%o (PARI) a_vector(n, s=2, t=0) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*sum(k=0, i-1, (s*k+t)^(i-k-1)*binomial(i-1, k)*v[k+1])); v;

%Y Cf. A000142, A395666.

%Y Cf. A397881, A397882.

%Y Cf. A397858.

%K nonn,new

%O 0,3

%A _Seiichi Manyama_, Jul 13 2026