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A173003 Antidiagonal triangle sequence based on recursion: f(n,a)=a*n*f(n-1,a)+f(n-2,a) 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A128749 A106579 A287318 * A294411 A274390 A244128

Adjacent sequences:  A173000 A173001 A173002 * A173004 A173005 A173006

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 07 2010

STATUS

approved

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Last modified May 25 11:51 EDT 2019. Contains 323553 sequences. (Running on oeis4.)