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 A021724 Expansion of 1/((1-x)(1-3x)(1-10x)(1-12x)). 1
 1, 26, 465, 7150, 101621, 1378026, 18123145, 233349350, 2958918141, 37094306626, 461004657425, 5690785933950, 69876732453061, 854393804284826, 10411455807073305, 126524771262956950, 1534170271000826381 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Bruno Berselli, May 08 2013: (Start) Naturally, the sequence is related to: A018207, 1/((1-3x)(1-10x)(1-12x)): A018207(n) = a(n)-a(n-1), n>0; A016267, 1/((1-x)(1-10x)(1-12x)): A016267(n) = a(n)-3*a(n-1), n>0; A016217, 1/((1-x)(1-3x)(1-12x)): A016217(n) = a(n)-10*a(n-1), n>0; A016215, 1/((1-x)(1-3x)(1-10x)): A016215(n) = a(n)-12*a(n-1), n>0; A016196, 1/((1-10x)(1-12x)): A016196(n) = a(n)-4*a(n-1)+3*a(n-2), n>1; A016147, 1/((1-3x)(1-12x)): A016147(n) = a(n)-11*a(n-1)+10*a(n-2), n>1; A016145, 1/((1-3x)(1-10x)): A016145(n) = a(n)-13*a(n-1)+12*a(n-2), n>1; A016125, 1/((1-x)(1-12x)): A016125(n) = a(n)-13*a(n-1)+30*a(n-2), n>1; A002275, x/((1-x)(1-10x)): A002275(n) = a(n-1)-15*a(n-2)+36*a(n-3), n>2; A003462, x/((1-x)(1-3x)): A003462(n) = a(n-1)-22*a(n-2)+120*a(n-3), n>2; A000012, 1/(1-x): A000012(n) = a(n)-25*a(n-1)+186*a(n-2)-360*a(n-3), n>2; A000244, 1/(1-3x): A000244(n) = a(n)-23*a(n-1)+142*a(n-2)-120*a(n-3), n>2; A011557, 1/(1-10x): A011557(n) = a(n)-16*a(n-1)+51*a(n-2)-36*a(n-3), n>2; A001021, 1/(1-12x): A001021(n) = a(n)-14*a(n-1)+43*a(n-2)-30*a(n-3), n>2. (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (26,-211,546,-360). FORMULA G.f.: 1/((1-x)*(1-3*x)*(1-10*x)*(1-12*x)). a(n) = -1/198 +3^(n+1)/14 -2^(n+2)*5^(n+3)/63 +2^(2n+5)*3^(n+1)/11. [Bruno Berselli, May 07 2013] MATHEMATICA CoefficientList[Series[1/((1 - x) (1 - 3 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* Bruno Berselli, May 07 2013 *) LinearRecurrence[{26, -211, 546, -360}, {1, 26, 465, 7150}, 120] (* Harvey P. Dale, Jul 06 2019 *) PROG (PARI) Vec(1/((1-x)*(1-3*x)*(1-10*x)*(1-12*x))+O(x^20)) \\ Bruno Berselli, May 07 2013 (Magma) m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-10*x)*(1-12*x)))); // Bruno Berselli, May 07 2013 CROSSREFS Cf. A000012, A000244, A001021, A002275, A003462, A011557, A016125, A016145, A016147, A016196, A016215, A016217, A016267, A018207. Sequence in context: A158428 A158425 A020566 * A019747 A163740 A021334 Adjacent sequences: A021721 A021722 A021723 * A021725 A021726 A021727 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 5 21:40 EST 2022. Contains 358594 sequences. (Running on oeis4.)