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A129126 Ninth diagonal of table A060850 counting partitions into parts of k kinds. 1
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; text; internal format)
OFFSET

1,1

COMMENTS

A slightly different method of calculating A129126 is described in A128627.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

From Alois P. Heinz, Oct 17 2008: (Start)

G.f.: x*(x-2)*(2*x^5-14*x^4+35*x^3-32*x^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); # Alois P. Heinz, Oct 16 2008

# second Maple program:

a:= n-> n*(n+6)*(n+3)*(n+1)*(4200+(9994+(1571+(74+n)*n)*n)*n)/40320:

seq(a(n), n=1..40);  # Alois P. Heinz, Oct 17 2008

CROSSREFS

Cf. A000041, A000712, A000716, A023003, A060850, A128627, A128629.

Sequence in context: A248495 A248496 A229367 * A231749 A072040 A022682

Adjacent sequences:  A129123 A129124 A129125 * A129127 A129128 A129129

KEYWORD

nonn,uned

AUTHOR

Alford Arnold, Apr 03 2007

EXTENSIONS

More terms from Alois P. Heinz, Oct 16 2008

STATUS

approved

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Last modified December 11 18:19 EST 2019. Contains 329925 sequences. (Running on oeis4.)