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Search: id:A136205
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| A136205 |
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Square array read by antidiagonals: T(m,n) = H(n,m2)*(2m)!/(2m+2n-1). H(0,m) = 1/m, for all positive integers m. H(n,m) = sum{k=1 to m} H(n-1,k). |
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1
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| 1, 1, 2, 1, 10, 24, 1, 22, 252, 720, 1, 38, 892, 12176, 40320, 1, 58, 2232, 60336, 966240, 3628800, 1, 82, 4632, 199440, 6202080, 114341760, 479001600, 1, 110, 8524, 526256, 25598016, 905049216, 18897709824, 87178291200, 1, 142, 14412, 1197360
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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In the array, the first m is 1; the first n is 0.
Every term of the array is a positive integer.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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For n>=1, T(m,n) also equals (H(2m+n-1) - H(n-1)) * (2m+n-1)!/((2m+2n-1) (n-1)!), where H(k) = H(1,k), the kth harmonic number.
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EXAMPLE
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Array: (The upper-left-most terms is T(1,0).)
1, 2, 24, 720 (Row equals {(2m-2)!}.)
1, 10, 252 (Row equals {H(1,2m) (2m)!/(2m+1)}, where H(1,2m) = the (2m)th harmonic number.)
1, 22 (Row equals {H(2,2m)*(2m)!/(2m+3)}.)
1 (Row equals {H(3,2m)*(2m)!/(2m+5)}.
The column {T(1,n)} consists entirely of 1's.
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CROSSREFS
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Cf. A105954.
Cf. A090288, A010050, A114450.
Adjacent sequences: A136202 A136203 A136204 this_sequence A136206 A136207 A136208
Sequence in context: A151504 A151507 A151363 this_sequence A024433 A065624 A071926
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KEYWORD
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nonn,tabl
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AUTHOR
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Leroy Quet Mar 16 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2008
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