A117157 a(1)=a(2)=1; a(n) = a(n-1)*a(n-2) + a(n-3) + a(n-4) + ... + a(1) for n>2.

1, 1, 1, 2, 4, 11, 49, 548, 26872, 14725925, 395715057217, 5827270253948278214, 2305938581960065033611659323852, 13437327306087560724405450621249967248150551970959

Offset

1,4

Comments

Form the product of the previous two terms and then add all other previous terms.

Links

Table of n, a(n) for n=1..14.

Mathematica

f[s_] := Block[{}, Append[s, s[[ -1]]s[[ -2]] + Plus @@ Drop[s, -2]]]; Nest[f, {1, 1}, 12] (* Robert G. Wilson v, May 26 2006 *)

Prog

#include <stdio.h> #include <inttypes.h> int main (void) { int64_t n1=1; int64_t n2=1; int i; int64_t sum=0, next; printf("%lld, %lld, ", n1, n2); for (i=0; i<10; i++) { next=n1*n2+sum; sum+=n1; n1=n2; n2=next; printf("%lld, ", n2); } }
(PARI) {m=14; print1(a=1, ", ", b=1, ", "); v=[]; for(n=3, m, print1(k=a*b+sum(j=1, #v, v[j]), ", "); v=concat(v, a); a=b; b=k)} \\ Klaus Brockhaus

Crossrefs

Cf. A117030.

Sequence in context: A091240 A068488 A096119 * A267013 A376918 A318532

Adjacent sequences: A117154 A117155 A117156 * A117158 A117159 A117160

Keyword

nonn

Author

Gabriel Finch (salsaman(AT)xs4all.nl), Apr 21 2006

Extensions

a(13) and a(14) from Klaus Brockhaus, Apr 27 2006

Status

approved