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 A080423 a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(n+15)*3^n/360. 6
 1, 16, 153, 1134, 7182, 40824, 214326, 1058508, 4979799, 22517352, 98513415, 419129802, 1741000716, 7083045648, 28296044604, 111232727064, 431026817373, 1648861601184, 6234757929477, 23328137324646, 86451332438394, 317576323243080, 1157228874847890, 4185605730648420 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (18,-135,540,-1215,1458,-729). FORMULA G.f.: (1-2*x)/(1-3*x)^6. From G. C. Greubel, Dec 22 2023: (Start) a(n) = A136158(n+5, 5). E.g.f.: (1/40)*(40 + 520*x + 1320*x^2 + 1080*x^3 + 315*x^4 + 27*x^5)*exp(3*x). (End) From Amiram Eldar, Jan 11 2024: (Start) Sum_{n>=0} 1/a(n) = 215084880*log(3/2)/1001 - 99766344351/1145144. Sum_{n>=0} (-1)^n/a(n) = 216218880*log(4/3)/1001 - 498108421095/8016008. (End) MATHEMATICA CoefficientList[Series[(1 - 2 x) / (1 - 3 x)^6, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *) Table[3^n*(n+15)*Binomial[n+4, 4]/15, {n, 0, 30}] (* G. C. Greubel, Dec 22 2023 *) PROG (Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(n+15)*3^n/360: n in [0..30]]; // Vincenzo Librandi, Aug 05 2013 (SageMath) [3^n*(n+15)*binomial(n+4, 4)/15 for n in range(31)] # G. C. Greubel, Dec 22 2023 CROSSREFS T(n, 5) of triangle A080419. Cf. A136158. Sequence in context: A224737 A076071 A096136 * A004313 A373293 A249981 Adjacent sequences: A080420 A080421 A080422 * A080424 A080425 A080426 KEYWORD easy,nonn AUTHOR Paul Barry, Feb 19 2003 STATUS approved

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Last modified September 9 13:46 EDT 2024. Contains 375764 sequences. (Running on oeis4.)