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URL: https://oeis.org/A021344

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A021344
Expansion of 1/((1-x)*(1-3*x)*(1-4*x)*(1-5*x)).
1
1, 13, 110, 770, 4851, 28623, 161680, 885940, 4749701, 25058033, 130616850, 674656710, 3460370551, 17652592243, 89673093620, 454027521080, 2292850387401, 11555296775253, 58141244359990, 292167007127050, 1466683407120251, 7356826212071063, 36877814837823960, 184763950513762620
OFFSET
0,2
COMMENTS
Sum of products 1^(p1)*3^(p2)*4^(p3)*5^(p4) where p1+p2+p3+p4=n, pi nonnegative integers Enrique Navarrete, Mar 21 2026
FORMULA
a(0)=1, a(1)=13, a(2)=110, a(3)=770; for n>3, a(n) = 13*a(n-1) -59*a(n-2) +107*a(n-3)-60*a(n-4). - Vincenzo Librandi, Jul 09 2013
a(0)=1, a(1)=13; for n>1, a(n) = 9*a(n-1) -20*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013
From Enrique Navarrete, Mar 21 2026: (Start)
a(n) = (1/24)*(375*5^n - 512*4^n + 162*3^n - 1).
a(n) = (1/2)*Sum_{k=1..n+2} A245019(k).
E.g.f.: (1/24)*(375*exp(5*x) - 512*exp(4*x) + 162*exp(3*x) - exp(x)). (End)
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 5 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 09 2013 *)
LinearRecurrence[{13, -59, 107, -60}, {1, 13, 110, 770}, 20] (* Harvey P. Dale, May 10 2024 *)
PROG
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-5*x)))); // Vincenzo Librandi, Jul 09 2013
(Magma) I:=[1, 13, 110, 770]; [n le 4 select I[n] else 13*Self(n-1)-59*Self(n-2)+107*Self(n-3)-60*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013
CROSSREFS
Partial sums of A016753.
Cf. A245019.
Sequence in context: A075143 A005769 A042941 * A119744 A295204 A298228
KEYWORD
nonn,easy,changed
STATUS
approved