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A173004 Antidiagonal triangle sequence based on recursion: f(n,a)=a*f(n-1,a)+n*f(n-2,a) 0
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A118343 A226031 A244116

Adjacent sequences:  A173001 A173002 A173003 * A173005 A173006 A173007

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 07 2010

STATUS

approved

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Last modified May 26 22:57 EDT 2019. Contains 323597 sequences. (Running on oeis4.)