cp's OEIS Frontend

A227366 a(0)=1, a(n+1) = a(n) + a(n-1)*a(n-2) + a(n-3)*a(n-4)*a(n-5) + a(n-6)*a(n-7)*a(n-8)*a(n-9) + ... + ...*a(0).

%I A227366 #14 May 04 2021 08:48:28
%S A227366 1,1,2,3,6,13,33,118,584,4714,76206,2879841,364389490,220150411628,
%T A227366 1049813737275512,80222580570107370160,231117086585854944888597249,
%U A227366 84218767584329653007205530276477742,18540809099930664963747242025045529905738135516
%N A227366 a(0)=1, a(n+1) = a(n) + a(n-1)*a(n-2) + a(n-3)*a(n-4)*a(n-5) + a(n-6)*a(n-7)*a(n-8)*a(n-9) + ... + ...*a(0).
%e A227366 a(1) = a(0) = 1
%e A227366 a(2) = a(1) + a(0) = 2
%e A227366 a(3) = a(2) + a(1)*a(0) = 3
%e A227366 a(4) = a(3) + a(2)*a(1) + a(0) = 3 + 2 + 1 = 6
%e A227366 a(5) = a(4) + a(3)*a(2) + a(1)*a(0) = 6 + 3*2 + 1 = 13
%o A227366 (Python)
%o A227366 a = [1]*99
%o A227366 for n in range(20):
%o A227366   sum = i = 0
%o A227366   k = 1
%o A227366   while i<=n:
%o A227366     product = 1
%o A227366     for x in range(k):
%o A227366       product *= a[n-i]
%o A227366       i += 1
%o A227366       if i>n: break
%o A227366     sum += product
%o A227366     k += 1
%o A227366   a[n+1] = sum
%o A227366   print(str(a[n]),end=',')
%Y A227366 Cf. A227363, A227364, A227365, A227367.
%K A227366 nonn
%O A227366 0,3
%A A227366 _Alex Ratushnyak_, Jul 08 2013