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).

1, 1, 2, 3, 6, 13, 33, 118, 584, 4714, 76206, 2879841, 364389490, 220150411628, 1049813737275512, 80222580570107370160, 231117086585854944888597249, 84218767584329653007205530276477742, 18540809099930664963747242025045529905738135516

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Example

a(1) = a(0) = 1
a(2) = a(1) + a(0) = 2
a(3) = a(2) + a(1)*a(0) = 3
a(4) = a(3) + a(2)*a(1) + a(0) = 3 + 2 + 1 = 6
a(5) = a(4) + a(3)*a(2) + a(1)*a(0) = 6 + 3*2 + 1 = 13

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[n-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, A227367.

Sequence in context: A296531 A220699 A202086 * A171878 A117403 A002877

Adjacent sequences: A227363 A227364 A227365 * A227367 A227368 A227369

Keyword

nonn

Author

Alex Ratushnyak, Jul 08 2013

Status

approved