A173004 Antidiagonal triangle sequence based on recursion: f(n,a)=a*f(n-1,a)+n*f(n-2,a)

0, 0, 1, 0, 1, 1, 0, 1, 2, 4, 0, 1, 3, 7, 8, 0, 1, 4, 12, 22, 28, 0, 1, 5, 19, 48, 79, 76, 0, 1, 6, 28, 92, 204, 290, 272, 0, 1, 7, 39, 160, 463, 900, 1133, 880, 0, 1, 8, 52, 258, 940, 2404, 4128, 4586, 3328

Offset

0,9

Comments

Row sums are:

{0, 1, 2, 7, 19, 67, 228, 893, 3583, 15705,...}.

Links

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

Formula

f(n,a)=a*f(n-1,a)+n*f(n-2,a);

t(n,m)=antidiagonal(f(n,a))

Example

{0},
{0, 1},
{0, 1, 1},
{0, 1, 2, 4},
{0, 1, 3, 7, 8},
{0, 1, 4, 12, 22, 28},
{0, 1, 5, 19, 48, 79, 76},
{0, 1, 6, 28, 92, 204, 290, 272},
{0, 1, 7, 39, 160, 463, 900, 1133, 880},
{0, 1, 8, 52, 258, 940, 2404, 4128, 4586, 3328}

Mathematica

f[0, a_] := 0; f[1, a_] := 1;
f[n_, a_] := f[n, a] = a*f[n - 1, a] + n*f[n - 2, a];
m1 = Table[f[n, a], {n, 0, 10}, {a, 1, 11}];
Table[Table[m1[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
Flatten[%]

Crossrefs

Sequence in context: A083741 A258761 A256245 * A378323 A378290 A118343

Adjacent sequences: A173001 A173002 A173003 * A173005 A173006 A173007

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Feb 07 2010

Status

approved