cp's OEIS Frontend

A227367 a(0)=1, a(n+1) = a(0) + a(1)*a(2) + a(3)*a(4)*a(5) + a(6)*a(7)*a(8)*a(9) + ... + ...*a(n).

%I A227367 #14 May 04 2021 08:48:19
%S A227367 1,1,2,3,6,21,381,762,290703,84397476747,7122934049104967061783,
%T A227367 14245868098209934123566,
%U A227367 101472378935797762635619628499635817245339961,10296643686890133479148472187437767614663729545766251948487237380959682684821520304732841
%N A227367 a(0)=1, a(n+1) = a(0) + a(1)*a(2) + a(3)*a(4)*a(5) + a(6)*a(7)*a(8)*a(9) + ... + ...*a(n).
%e A227367 a(1) = a(0) = 1
%e A227367 a(2) = a(0) + a(1) = 2
%e A227367 a(3) = a(0) + a(1)*a(2) = 3
%e A227367 a(4) = a(0) + a(1)*a(2) + a(3) = 1 + 2 + 3 = 6
%e A227367 a(5) = a(0) + a(1)*a(2) + a(3)*a(4) = 1 + 2 + 18 = 21
%e A227367 a(6) = a(0) + a(1)*a(2) + a(3)*a(4)*a(5) = 1 + 2 + 18*21 = 381
%o A227367 (Python)
%o A227367 a = [1]*99
%o A227367 for n in range(20):
%o A227367   sum = i = 0
%o A227367   k = 1
%o A227367   while i<=n:
%o A227367     product = 1
%o A227367     for x in range(k):
%o A227367       product *= a[i]
%o A227367       i += 1
%o A227367       if i>n: break
%o A227367     sum += product
%o A227367     k += 1
%o A227367   a[n+1] = sum
%o A227367   print(str(a[n]),end=',')
%Y A227367 Cf. A227363, A227364, A227365, A227366.
%K A227367 nonn
%O A227367 0,3
%A A227367 _Alex Ratushnyak_, Jul 08 2013