A059922 - OEIS

A059922

Each term in the table is the product of the two terms above it + 1.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 10, 4, 1, 1, 5, 41, 41, 5, 1, 1, 6, 206, 1682, 206, 6, 1, 1, 7, 1237, 346493, 346493, 1237, 7, 1, 1, 8, 8660, 428611842, 120057399050, 428611842, 8660, 8, 1, 1, 9, 69281, 3711778551721, 51458022952549550101, 51458022952549550101, 3711778551721, 69281, 9, 1

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OFFSET

0,5

COMMENTS

Row sums are A059731.

LINKS

Table of n, a(n) for n=0..54.

S. Kak, The Golden Mean and the Physics of Aesthetics

FORMULA

a(m, n) = a(m-1, n-1)*a(m-1, n)+1, a(0, 0) = 1, a(m, n) = 0 iff n>m or n<0.

EXAMPLE

Triangle begins:

1,1;

1,2,1;

1,3,3,1;

1,4,10,4,1; ...

MAPLE

aaa := proc(m, n) option remember; if n>m or n<0 then 0; elif m=0 and n=0 then 1; else aaa(m-1, n-1)*aaa(m-1, n)+1; fi; end;

MATHEMATICA

a[0, 0] = 1; a[m_, n_] /; (n > m || n < 0) = 0; a[m_, n_] := a[m, n] = a[m-1, n-1]*a[m-1, n] + 1; Table[a[m, n], {m, 0, 9}, {n, 0, m}] // Flatten (* Jean-François Alcover, Sep 10 2013 *)

PROG

(Haskell)

a059922 n k = a059922_tabl !! n !! k

a059922_flattened = concat a059922_tabl

a059922_tabl = iterate (\rs ->

zipWith (+) (0 : reverse (0 : replicate (length rs - 1) 1))

$ zipWith (*) ([1] ++ rs) (rs ++ [1])) [1]

a059730 n = a059922_tabl !! n !! (n-3)

a059731 n = sum (a059922_tabl !! n)

a059732 n = a059922_tabl !! (2*n) !! n

a059733 n = a059922_tabl !! n !! n `div` 2

-- Reinhard Zumkeller, Jun 22 2011