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A006230
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Bitriangular permutations.
(Formerly M4902)
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1
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1, 13, 73, 301, 1081, 3613, 11593, 36301, 111961, 342013, 1038313, 3139501, 9467641, 28501213, 85700233, 257493901, 773268121, 2321377213, 6967277353, 20908123501
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,2
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REFERENCES
| I. Kaplansky and J. Riordan, The problem of the rooks and its applications, Duke Math. J., 13 (1946), 259-268.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| a(n) = 12*S(n-2) + 1, with S(n)=A000392(n) the Stirling numbers of second kind, 3rd column. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
a(n+3) = sum_{i=1..3} A008277(n,i) * A008277(3,i) * i!^2. - Brian Parsonnet, Feb 25 2011
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MAPLE
| A006230:=-(z+1)*(6*z+1)/(z-1)/(3*z-1)/(2*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| 12*StirlingS2[n+1, 3]+1; (* Brian Parsonnet, Feb 25 2011 *)
Sum[ StirlingS2[n, i] * StirlingS2[ 3, i ] * i!^2, {i, 3} ]; (* alternative, Brian Parsonnet, Feb 25 2011 *)
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CROSSREFS
| A136301 (row 4).
Sequence in context: A081586 A143008 A107963 * A066110 A020527 A146618
Adjacent sequences: A006227 A006228 A006229 * A006231 A006232 A006233
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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