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A107600
Column 5 of array illustrated in A089574 and related to A034261.
11
1, 18, 101, 357, 978, 2274, 4711, 8954, 15915, 26806, 43197, 67079, 100932, 147798, 211359, 296020, 406997, 550410, 733381, 964137, 1252118, 1608090, 2044263, 2574414, 3214015, 3980366, 4892733, 5972491, 7243272, 8731118, 10464639
OFFSET
9,2
COMMENTS
The sequences in A089574 count ordered partitions. Sequence A001296 can be associated with 9 = 3+3+3. Six times sequence A005585, associated with 10 = 3+3+2+2. The other three sequences comprising A107600 are generated in A034261 and can be associated with 10 = 5 + 5 = 4 + 4 + 2 = 2 + 2 + 2 + 2 + 2.
FORMULA
G.f.: (x^5 -5*x^4 +7*x^3 +4*x^2 -11*x -1) *x^9 /(x-1)^7. - Alois P. Heinz, Nov 06 2009
EXAMPLE
A107600(n) can be constructed from five other sequences as follows:
1...7...25...65...140.......A001296
....1...11...56...196.......A034264
....6...42..162...462.......6.*.A005585.
....3...18...60...150.......A006011
....1....5...14....30.......A000330
therefore
1..18..101..357...978.......A107600
MAPLE
a:= n-> `if` (n<9, 0, (92292 +(-6580 +(-5745 +(1535 +(-147+5*n) *n) *n) *n) *n) *n /720 -218): seq(a(n), n=9..45); # Alois P. Heinz, Nov 06 2009
MATHEMATICA
Select[CoefficientList[Series[(x^5-5x^4+7x^3+4x^2-11x-1)x^9/(x-1)^7, {x, 0, 50}], x], #>0&] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 18, 101, 357, 978, 2274, 4711}, 42] (* Harvey P. Dale, May 01 2011 *)
KEYWORD
easy,nonn
AUTHOR
Alford Arnold, May 17 2005
EXTENSIONS
More terms from Alois P. Heinz, Nov 06 2009
STATUS
approved