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).

1, 1, 2, 3, 6, 21, 381, 762, 290703, 84397476747, 7122934049104967061783, 14245868098209934123566, 101472378935797762635619628499635817245339961, 10296643686890133479148472187437767614663729545766251948487237380959682684821520304732841

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Example

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

Prog

(Python)
a = [1]*99
for n in range(20):
  sum = i = 0
  k = 1
  while i<=n:
    product = 1
    for x in range(k):
      product *= a[i]
      i += 1
      if i>n: break
    sum += product
    k += 1
  a[n+1] = sum
  print(str(a[n]), end=', ')

Crossrefs

Cf. A227363, A227364, A227365, A227366.

Sequence in context: A303224 A007501 A369996 * A270397 A278106 A015773

Adjacent sequences: A227364 A227365 A227366 * A227368 A227369 A227370

Keyword

nonn

Author

Alex Ratushnyak, Jul 08 2013

Status

approved