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A110112
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Square array of numbers associated to the recurrences a(k)=a(k-1)+n*a(k-2), read by antidiagonals.
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0
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1, 1, 1, 1, 3, 1, 1, 15, 5, 1, 1, 60, 55, 7, 1, 1, 260, 385, 133, 9, 1, 1, 1092, 3311, 1330, 261, 11, 1, 1, 4641, 25585, 18430, 3393, 451, 13, 1, 1, 19635, 208335, 210490, 68237, 7216, 715, 15, 1, 1, 83215, 1652145, 2673223, 1037673, 197456, 13585, 1065, 17, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Rows include A001655, (-1)^n*A015266(n+3), A110111.
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FORMULA
| Number square T(n, k)=a(n, k+1)a(n, k+2)a(n, k+3)/(n+1) where a(n, k) is the solution to a(n, k)=a(n, k-1)+n*a(n, k-2) with a(n, 0)=0, a(n, 1)=1. Row n has g.f. 1/((1+n*x-n^3*x^2)(1-(3n+1)x-n^3*x^2));
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EXAMPLE
| Rows begin
1,1,1,1,1,....
1,3,15,60,260,....
1,5,55,385,3311,25585,...
1,7,133,1330,18430,210490,...
1,9,261,3393,68237,1037673,...
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CROSSREFS
| Cf. A083856.
Sequence in context: A072285 A144269 A144270 * A176225 A173917 A174410
Adjacent sequences: A110109 A110110 A110111 * A110113 A110114 A110115
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 12 2005
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