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A021714
Expansion of 1/((1-x)(1-3x)(1-10x)(1-11x)).
1
1, 25, 428, 6278, 84879, 1092243, 13601506, 165488176, 1979095877, 23357343581, 272803757304, 3159571375194, 36342586372795, 415641464948839, 4730786270092622, 53625950549096132, 605758471885400433
OFFSET
0,2
FORMULA
G.f.: 1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x)).
a(n) = -1/180 +3^(n+3)/112 -10^(n+3)/63 +11^(n+3)/80. [Bruno Berselli, May 07 2013]
a(n)-11*a(n-1) = A016215(n). [Bruno Berselli, May 08 2013]
MATHEMATICA
CoefficientList[Series[1/((1 - x) (1 - 3 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* Bruno Berselli, May 07 2013 *)
LinearRecurrence[{25, -197, 503, -330}, {1, 25, 428, 6278}, 20] (* Harvey P. Dale, Jan 16 2024 *)
PROG
(PARI) Vec(1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x))+O(x^20)) \\ Bruno Berselli, May 07 2013
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x)))); // Bruno Berselli, May 07 2013
CROSSREFS
Cf. A016215, A018206 (first differences).
Sequence in context: A020499 A226712 A020577 * A056090 A020448 A203544
KEYWORD
nonn,easy
AUTHOR
STATUS
approved