A129126 - OEIS

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A129126

Ninth diagonal of table A060850 counting partitions into parts of k kinds.

22, 185, 810, 2580, 6765, 15525, 32305, 62337, 113265, 195910, 325193, 521235, 810654, 1228080, 1817910, 2636326, 3753600, 5256711, 7252300, 9869990, 13266099, 17627775, 23177583, 30178575, 38939875, 49822812, 63247635 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`A slightly different method of calculating A129126 is described in A128627`
	FORMULA	`Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008: (Start)` `G.f.: x(x-2)(2x^5-14x^4+35x^3-32x^2-x+11)/(x-1)^9.` `a (n) = n(n+6)(n+3)(n+1)(4200+(9994+(1571+(74+n)n)n)*n)/40320. (End)`
	EXAMPLE	`From A128629 we can construct the table below:` `...Deg..#...Associated.sequence.........` `8...1...1...1...2...3...4` `44...2...3...1...3...6...10` `53...11...4...1...4...9...16` `62...11...4...1...4...9...16` `71...11...4...1...4...9...16` `332...12...6...1...6...18...40` `422...12...6...1...6...18...40` `431...111...8...1...8...27...64` `521...111...8...1...8...27...64` `611...12...6...1...6...18...40` `2222...4...7...1...5...15...35` `3221...112...12...1...12...54...160` `3311...22...9...1...9...36...100` `4211...112...12...1...12...54...160` `5111...13...10...1...8...30...80` `22211...23...15...1...12...60...200` `32111...113...20...1...16...90...320` `41111...14...14...1...10...45...140` `221111...24...21...1...15...90...350` `311111...15...22...1...12...63...224` `1111111...8...19...1...9...45...165` `2111111...16...26...1...14...84...336` `Summing we get 22,185,810,2580,...`
	MAPLE	with (numtheory): b:=proc(n) option remember; local d, j; `if` (n=0, 1, add (add (d, d=divisors(j)) b(n-j), j=1..n)/n) end: A:= proc (n) option remember; local k; `if` (n=0, x, expand (add (b(k-1) A(n-k) x^(k-1), k=1..n))) end: a:= n-> coeftayl (A(n+8), x=0, 9): seq (a(n), n=1..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 16 2008] `a:= n-> n(n+6)(n+3)(n+1)(4200+(9994+(1571+(74+n)n)n)n)/40320: seq (a(n), n=1..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]`
	CROSSREFS	`Cf. A000041 A000712 A000716 A023003 A060850 A128627 A128629.` `Sequence in context: A197496 A107969 A191012 * A072040 A022682 A107959` `Adjacent sequences: A129123 A129124 A129125 * A129127 A129128 A129129`
	KEYWORD	`nonn,tabf,uned`
	AUTHOR	`Alford Arnold (Alford1940(AT)aol.com), Apr 03 2007`
	EXTENSIONS	`More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 16 2008`

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Last modified February 17 16:49 EST 2012. Contains 206058 sequences.