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A081297
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Square array of solutions of a family of recurrences.
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5
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1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 5, 1, 1, 1, 13, 13, 11, 1, 1, 1, 21, 25, 55, 21, 1, 1, 1, 31, 41, 181, 133, 43, 1, 1, 1, 43, 61, 461, 481, 463, 85, 1, 1, 1, 57, 85, 991, 1281, 2653, 1261, 171, 1, 1, 1, 73, 113, 1891, 2821, 10501, 8425, 4039, 341, 1, 1, 1, 91, 145, 3305
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Rows of the array give solutions to the recurrences a(n)=a(n-1)+k(k-1)a(n-2), a(0)=a(1)=1. Rows include A001045, A015441, A053404, A053428, A053430. Columns include A002061, A001844, A072025. Diagonals include A081298, A081299, A081300, A081301, A081302.
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FORMULA
| T(k, n)=((k+1)^(n+1)-(-k)^(n+1))/(2k+1). Rows of the array have have have g.f. 1/((1+kx)(1-(k+1)x)).
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EXAMPLE
| Rows begin
1.1.1..1..1...1....
1.1.3..5..11..21...
1.1.7..13.55..133..
1.1.13.25.181.481..
1.1.21.41.461.1281.
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CROSSREFS
| Sequence in context: A068845 A152884 A204984 * A110180 A005765 A156535
Adjacent sequences: A081294 A081295 A081296 * A081298 A081299 A081300
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 17 2003
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