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A022033
Expansion of 1/((1-x)(1-5x)(1-6x)(1-7x)).
1
1, 19, 236, 2426, 22407, 193305, 1591402, 12667072, 98321333, 748601711, 5614533288, 41608696038, 305407826179, 2224262385637, 16095911708294, 115865978983724, 830420169903345, 5930044765743483, 42217703190306820
OFFSET
0,2
FORMULA
a(n) = (10*7^(n+3)-24*6^(n+3)+15*5^(n+3)-1)/120. - Yahia Kahloune, May 22 2013.
a(0)=1, a(1)=19, a(2)=236, a(3)=2426; for n>3, a(n) = 19*a(n-1) -125*a(n-2) +317*a(n-3) -210*a(n-4). - Vincenzo Librandi, Jul 12 2013
a(0)=1, a(1)=19; for n>1, a(n) = 13*a(n-1) -42*a(n-2) +(5^n-1)/4. - Vincenzo Librandi, Jul 12 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 6 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)
PROG
(Magma) I:=[1, 19, 236, 2426]; [n le 4 select I[n] else 19*Self(n-1)-125*Self(n-2)+317*Self(n-3)-210*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-6*x)*(1-7*x)))); // Vincenzo Librandi, Jul 12 2013
CROSSREFS
Sequence in context: A025960 A152494 A171158 * A025938 A229026 A114757
KEYWORD
nonn,easy
AUTHOR
STATUS
approved