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 A081901 A sequence related to binomial(n+5, 5). 2
 1, 8, 49, 262, 1286, 5944, 26262, 111996, 464103, 1877904, 7446735, 29021490, 111405780, 422003520, 1579757580, 5851519704, 21468622077, 78087814776, 281798184573, 1009617794334, 3593281988754, 12710491403112, 44705999907666 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A055852. 2nd binomial transform of binomial(n+5, 5). 3rd binomial transform of (1,5,10,10,5,1,0,0,0,...). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (18,-135,540,-1215,1458,-729). FORMULA a(n) = 3^n*(n^5 + 65*n^4 + 1385*n^3 + 11575*n^2 + 35574*n + 29160)/29160. G.f.: (1 - 2*x)^5/(1 - 3*x)^6. E.g.f.: (120 + 600*x + 600*x^2 + 200*x^3 + 25*x^4 + x^5)*exp(3*x)/120. - G. C. Greubel, Oct 18 2018 MATHEMATICA LinearRecurrence[{18, -135, 540, -1215, 1458, -729}, {1, 8, 49, 262, 1286, 5944}, 50] (* G. C. Greubel, Oct 18 2018 *) PROG (PARI) x='x+O('x^30); Vec((1-2*x)^5/(1-3*x)^6) \\ G. C. Greubel, Oct 18 2018 (Magma) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^5/(1-3*x)^6)); // G. C. Greubel, Oct 18 2018 CROSSREFS Cf. A081902. Sequence in context: A354558 A344321 A166789 * A283686 A026389 A005059 Adjacent sequences: A081898 A081899 A081900 * A081902 A081903 A081904 KEYWORD nonn,easy AUTHOR Paul Barry, Mar 31 2003 STATUS approved

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Last modified March 23 16:16 EDT 2023. Contains 361445 sequences. (Running on oeis4.)