A021874 Expansion of 1/((1-x) * (1-4*x) * (1-7*x) * (1-10*x)).
1, 22, 325, 4070, 46781, 511742, 5430405, 56516790, 580744461, 5916830062, 59935396885, 604729235110, 6084941584541, 61113049957982, 612976296281765, 6142684971387030, 61517309500479021, 615806336417543502, 6162496145690677045, 61655991294017340550, 616777123265962899901
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (22,-159,418,-280).
Programs
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Mathematica
CoefficientList[Series[1 / ((1 - x) (1 - 4 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *) LinearRecurrence[{22,-159,418,-280},{1,22,325,4070},30] (* Harvey P. Dale, May 13 2018 *)
Formula
a(n) = (10^(n+3) - 3*7^(n+3) + 3*4^(n+3) - 1)/162. - Yahia Kahloune, Jul 05 2013
E.g.f.: exp(x)*(1000*exp(9*x) - 1029*exp(6*x) + 192*exp(3*x) - 1)/(3!*3^3). This is d^3/dx^3 exp(x)*(exp(3*x - 1))^3/(3!*3^3); see also column m=3 of A282629 divided by 3^3. The o.g.f. is given in the name. - Wolfdieter Lang, Apr 08 2017
a(n) = Sum_{k=0..n} 3^k * binomial(n+3,k+3) * Stirling2(k+3,3). - Seiichi Manyama, May 03 2025