A173003 Antidiagonal triangle sequence based on recursion: f(n,a)=a*n*f(n-1,a)+f(n-2,a)

0, 0, 1, 0, 1, 2, 0, 1, 4, 7, 0, 1, 6, 25, 30, 0, 1, 8, 55, 204, 157, 0, 1, 10, 97, 666, 2065, 972, 0, 1, 12, 151, 1560, 10045, 24984, 6961, 0, 1, 14, 217, 3030, 31297, 181476, 351841, 56660, 0, 1, 16, 295, 5220, 75901, 752688, 3821041, 5654440, 516901

Offset

0,6

Comments

Row sums are:

{0, 1, 3, 12, 62, 425, 3811, 43714, 624536, 10826503,...}.

Links

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

Formula

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

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

Example

{0},
{0, 1},
{0, 1, 2},
{0, 1, 4, 7},
{0, 1, 6, 25, 30},
{0, 1, 8, 55, 204, 157},
{0, 1, 10, 97, 666, 2065, 972},
{0, 1, 12, 151, 1560, 10045, 24984, 6961},
{0, 1, 14, 217, 3030, 31297, 181476, 351841, 56660},
{0, 1, 16, 295, 5220, 75901, 752688, 3821041, 5654440, 516901}

Mathematica

f[0, a_] := 0; f[1, a_] := 1;
f[n_, a_] := f[n, a] = a*n*f[n - 1, a] + 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: A287318 A329020 A351640 * A378236 A335461 A294411

Adjacent sequences: A173000 A173001 A173002 * A173004 A173005 A173006

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Feb 07 2010

Status

approved