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A257464 Number of factorizations of m^n into 3 factors, where m is a product of exactly 3 distinct primes and each factor is a product of n primes (counted with multiplicity). 2
1, 1, 5, 10, 23, 40, 73, 114, 180, 262, 379, 521, 712, 938, 1228, 1567, 1986, 2469, 3052, 3715, 4499, 5383, 6410, 7558, 8875, 10335, 11991, 13816, 15865, 18110, 20611, 23336, 26350, 29620, 33213, 37095, 41338, 45904, 50870, 56197, 61964, 68131, 74782, 81873 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Alexander V. Karpov, An Informational Basis for Voting Rules, NRU Higher School of Economics. Series WP BRP "Economics/EC". 2018. No. 188.

P. A. MacMahon, Combinations derived from m identical sets of n different letters and their connexion with general magic squares, Proc. London Math. Soc., 17 (1917), 25-41. This sequence is column 3 of table f(m,n) on page 40.

Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1).

FORMULA

G.f.: -(x^6-x^5+2*x^4+2*x^3+2*x^2-x+1)/((x^2+x+1)*(x+1)^2*(x-1)^5).

EXAMPLE

a(2) = 5: (2*3*5)^2 = 900 = 10*10*9 = 15*10*6 = 15*15*4 = 25*6*6 = 25*9*4.

a(4) = 23: (2*3*5)^4 = 810000 = 100*90*90 = 100*100*81 = 135*100*60 = 150*90*60 = 150*100*54 = 150*135*40 = 150*150*36 = 225*60*60 = 225*90*40 = 225*100*36 = 225*150*24 = 225*225*16 = 250*60*54 = 250*81*40 = 250*90*36 = 250*135*24 = 375*54*40 = 375*60*36 = 375*90*24 = 375*135*16 = 625*36*36 = 625*54*24 = 625*81*16.

MAPLE

a:= n-> coeff(series(-(x^6-x^5+2*x^4+2*x^3+2*x^2-x+1)/

        ((x^2+x+1)*(x+1)^2*(x-1)^5), x, n+1), x, n):

seq(a(n), n=0..60);

MATHEMATICA

CoefficientList[Series[-(x^6 - x^5 + 2 x^4 + 2 x^3 + 2 x^2 - x + 1)/((x^2 + x + 1) (x + 1)^2*(x - 1)^5), {x, 0, 43}], x] (* Michael De Vlieger, Jul 02 2018 *)

CROSSREFS

Row n=3 of A257463.

Sequence in context: A341638 A280002 A260567 * A295731 A175661 A197174

Adjacent sequences:  A257461 A257462 A257463 * A257465 A257466 A257467

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Apr 24 2015

STATUS

approved

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Last modified September 19 22:06 EDT 2021. Contains 347576 sequences. (Running on oeis4.)