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 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). 5

%I

%S 1,1,2,3,6,21,381,762,290703,84397476747,7122934049104967061783,

%T 14245868098209934123566,

%U 101472378935797762635619628499635817245339961,10296643686890133479148472187437767614663729545766251948487237380959682684821520304732841

%N 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 a(1) = a(0) = 1

%e a(2) = a(0) + a(1) = 2

%e a(3) = a(0) + a(1)*a(2) = 3

%e a(4) = a(0) + a(1)*a(2) + a(3) = 1 + 2 + 3 = 6

%e a(5) = a(0) + a(1)*a(2) + a(3)*a(4) = 1 + 2 + 18 = 21

%e a(6) = a(0) + a(1)*a(2) + a(3)*a(4)*a(5) = 1 + 2 + 18*21 = 381

%o (Python)

%o a = [1]*99

%o for n in range(20):

%o sum = i = 0

%o k = 1

%o while i<=n:

%o product = 1

%o for x in range(k):

%o product *= a[i]

%o i += 1

%o if i>n: break

%o sum += product

%o k += 1

%o a[n+1] = sum

%o print(str(a[n]),end=',')

%Y Cf. A227363, A227364, A227365, A227366.

%K nonn

%O 0,3

%A _Alex Ratushnyak_, Jul 08 2013

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Last modified September 22 09:47 EDT 2021. Contains 347606 sequences. (Running on oeis4.)