OFFSET
0,4
COMMENTS
This sequence is obtained by reversing the rows of the triangle A193738.
Except for the first term, this sequence gives the integers occurring in the song "One man went to mow".
LINKS
Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened
BBC, One man went to mow.
FORMULA
Write w(n,k) for the triangle at A193738. The current triangle is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....1
2....2....1
3....3....2....1
4....4....3....2...1
5....5....4....3...2...1
MATHEMATICA
z = 12;
p[0, x_] := 1
p[n_, x_] := x*p[n - 1, x] + 1; p[n_, 0] := p[n, x] /. x -> 0
q[n_, x_] := p[n, x]
t[n_, k_] := Coefficient[p[n, x], x^(n - k)];
t[n_, n_] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193738 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193739 *)
PROG
(Haskell)
a193738 n k = a193738_tabl !! n !! k
a193738_row n = a193738_tabl !! n
a193738_tabl = map reverse a193739_tabl
-- Reinhard Zumkeller, May 11 2013
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 04 2011
STATUS
approved