A108349 Main diagonal of Fibonacci-type array in which each term is equal to the term above multiplied by the term to the left.

1, 1, 2, 24, 25920, 1511654400000, 11882514930204672000000000000000, 3711388892113415871206624306663300844748800000000000000000000000000000000000

Offset

1,3

Comments

a(9) has 178 digits. - R. J. Mathar, Aug 26 2008

Links

Table of n, a(n) for n=1..8.

Formula

T(x, y) = T(x, y-1) * T(x-1, y) T(x, 1) = T(x-2, 1) + T(x-1, 1) T(1, 1) = 1 Direct Formula is T(x, x) for x = {1, 2, 3, 4...}

Example

a(4) = T(4,4) = 24; 24 = 2 * 12 = (1 * 2) * (2 * 6) = (1 * 2) * (2 * (2 * 3)) See chart:
1 1 2 3 5 ... (Fibonacci)
- 1 2 6 15 T(x, 2)
- - 2 12 90 T(x, 3)
- - - 24 1080 T(x, 4)

Maple

A108349T := proc(n, i) option remember ; if n = 1 then combinat[fibonacci](i) ; else procname(n-1, i)*procname(n-1, i+1) ; fi; end: A108349 := proc(n) A108349T(n, 1) ; end: for n from 1 to 9 do printf("%d, ", A108349(n)) ; od: # R. J. Mathar, Aug 26 2008

Crossrefs

Sequence in context: A137888 A229333 A338152 * A361431 A000722 A098679

Adjacent sequences: A108346 A108347 A108348 * A108350 A108351 A108352

Keyword

nonn,easy

Author

Brock J Nash (Brocknash(AT)wah.midco.net), Aug 17 2008

Extensions

a(6)-a(8) from R. J. Mathar, Aug 26 2008

Status

approved