id:A127080 - OEIS Search Results

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Infinite square array read by antidiagonals: Q(m, 0) = 1, Q(m, 1) = 1; Q(m, 2k) = (m - 2k + 1)*Q(m+1, 2k-1) - (2k-1)*Q(m+2, k-2), m*Q(m, 2k+1) = (m - 2k)*Q(m+1, 2k) - 2k(m+1)*Q(m+2, 2k-1).

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1, 1, 1, 1, 1, -2, 1, 1, -1, -5, 1, 1, 0, -4, 12, 1, 1, 1, -3, 3, 43, 1, 1, 2, -2, -4, 28, -120, 1, 1, 3, -1, -9, 15, -15, -531, 1, 1, 4, 0, -12, 4, 48, -288, 1680 (list; table; graph; listen)

	OFFSET	`0,6`
	REFERENCES	`V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.`
	FORMULA	`E.g.f.: Sum_{k >= 0} Q(m,2k) x^k/k! = (1+4x)^((m-1)/2)/(1+2x)^(m/2), Sum_{k >= 0} Q(m,2k+1) x^k/k! = (1+4x)^((m-2)/2)/(1+2x)^((m+1)/2).`
	EXAMPLE	`Array begins:` `1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...` `1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...` `-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...` `-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, ...` `12, 3, -4, -9, -12, -13, -12, -9, -4, 3, 12, 23, 36, ... (A127146)` `43, 28, 15, 4, -5, -12, -17, -20, -21, -20, -17, -12, -5, ... (A127147)` `-120, -15, 48, 75, 72, 45, 0, -57, -120, -183, -240, -285, -312, ... (A127148)` `-531, -288, -105, 24, 105, 144, 147, 120, 69, 0, -81, -168, -255, ...` `1680, 105, -624, -735, -432, 105, 720, 1281, 1680, 1833, 1680, 1185, 336, ...`
	CROSSREFS	`See A105937 for another version.` `Columns give A127137, A127138, A127144, A127145; rows give A127146, A127147, A127148.` `Sequence in context: A140274 A095231 A141471 this_sequence A014651 A082063 A099940` `Adjacent sequences: A127077 A127078 A127079 this_sequence A127081 A127082 A127083`
	KEYWORD	`sign,tabl`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com), Mar 24 2007`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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