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A107106 Divide A036039(n) by A036040(n). 4
1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 1, 24, 6, 2, 2, 1, 1, 1, 120, 24, 6, 4, 6, 2, 1, 2, 1, 1, 1, 720, 120, 24, 12, 24, 6, 4, 2, 6, 2, 1, 2, 1, 1, 1, 5040, 720, 120, 48, 36, 120, 24, 12, 6, 4, 24, 6, 4, 2, 1, 6, 2, 1, 2, 1, 1, 1, 40320, 5040, 720, 240, 144, 720, 120, 48, 36, 24, 12, 8, 120, 24, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A107107 gives the row sums. - R. J. Mathar, Aug 13 2007

This array is the first one (K=1) of a family of partition number arrays called M31(1). For M31(2) see A134133 = M_3(2)/M_3.

LINKS

Table of n, a(n) for n=1..81.

W. Lang, First 10 rows of the array and more.

FORMULA

a(n) = A036039(n) / A036040(n).

EXAMPLE

a(36) = 280/70 = 4.

As array: [1];[1,1];[2,1,1];[6,2,1,1,1];[24,6,2,2,1,1,1];[120,24,6,4,6,2,1,2,1,1,1];...

MAPLE

sortAbrSteg := proc(L1, L2) local i ; if nops(L1) < nops(L2) then RETURN(true) ; elif nops(L2) < nops(L1) then RETURN(false) ; else for i from 1 to nops(L1) do if op(i, L1) < op(i, L2) then RETURN(false) ; fi ; od ; RETURN(true) ; fi ; end: M2overM3 := proc(L) local n, k, an, resul; n := add(i, i=L) ; resul := 1 ; for k from 1 to n do an := add(1-min(abs(j-k), 1), j=L) ; resul := resul* (factorial(k-1))^an ; od ; end: A107106 := proc(n, k) local prts, m ; prts := combinat[partition](n) ; prts := sort(prts, sortAbrSteg) ; if k <= nops(prts) then M2overM3(op(k, prts)) ; else 0 ; fi ; end: for n from 1 to 10 do for k from 1 to combinat[numbpart](n) do a:=A107106(n, k) ; printf("%d, ", a) ; od; od ; # R. J. Mathar, Aug 13 2007

CROSSREFS

Cf. A107107.

Sequence in context: A123361 A265315 A179380 * A178249 A119502 A142156

Adjacent sequences:  A107103 A107104 A107105 * A107107 A107108 A107109

KEYWORD

easy,nonn,tabf

AUTHOR

Alford Arnold, May 12 2005

EXTENSIONS

Corrected and extended by R. J. Mathar, Aug 13 2007

a(75) and a(76) swapped (first 36, then 24) by Wolfdieter Lang, Sep 22 2008

STATUS

approved

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Last modified September 18 20:36 EDT 2019. Contains 327181 sequences. (Running on oeis4.)