A200542 - OEIS

%I #5 Mar 31 2012 10:23:14

%S 1,1,1,1,2,4,8,17,41,113,340,1070,3592,12979,50107,204325,875702,

%T 3947560,18724328,93137201,484066913,2623523381,14811843184,

%U 87000588266,530736806728

%N E.g.f. A(x) satisfies differential equation A'''(x)=A(x)+1/2*A(x)^2, A(0)=0, A'(0)=1, A''(0)=1, A'''(0)=1.

%F a(n)=n!*b(n), b(n)=1/(n*(n-1)*(n-2))*(i=1..n-4, b(n-3)+1/2*sum(b(i)*b(n-3-i))), n>3, b(1)=1, b(2)=1/2, b(3)=1/6.

%o (Maxima)

%o a(n):=if n<4 then 1/n! else 1/(n*(n-1)*(n-2))*(a(n-3)+1/2*sum(a(i)*a(n-3-i), i, 1, n-4));

%o makelist(n!*a(n), n, 1, 25);

%K nonn

%O 1,5

%A _Vladimir Kruchinin_, Nov 18 2011