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 A069080 a(n) = (2n+1)*(2n+2)*(2n+6)*(2n+7). 1
 84, 864, 3300, 8736, 18900, 35904, 62244, 100800, 154836, 228000, 324324, 448224, 604500, 798336, 1035300, 1321344, 1662804, 2066400, 2539236, 3088800, 3722964, 4449984, 5278500, 6217536, 7276500, 8465184, 9793764, 11272800, 12913236, 14726400, 16724004 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Konrad Knopp, Theory and application of infinite series, Dover, p. 268. LINKS Table of n, a(n) for n=0..30. Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series") Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA Sum_{n>=0} (-1)^n/a(n) = (Pi-149/60)/60. [Corrected by Amiram Eldar, Mar 08 2022] From Wesley Ivan Hurt, Mar 28 2015: (Start) G.f.: 12*(7 + 37*x - 15*x^2 + 3*x^3) / (1 - x)^5. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). a(n) = 16*n^4 + 128*n^3 + 332*n^2 + 304*n + 84. (End) Sum_{n>=0} 1/a(n) = 49/3600. - Amiram Eldar, Mar 08 2022 MAPLE A069080:=n->16*n^4 + 128*n^3 + 332*n^2 + 304*n + 84: seq(A069080(n), n=0..30); # Wesley Ivan Hurt, Mar 28 2015 MATHEMATICA CoefficientList[Series[12 (7 + 37x - 15x^2 + 3x^3)/(1 - x)^5, {x, 0, 30}], x] (* Wesley Ivan Hurt, Mar 28 2015 *) PROG (Magma) [(2*n+1)*(2*n+2)*(2*n+6)*(2*n+7) : n in [0..30]]; // Wesley Ivan Hurt, Mar 28 2015 (PARI) Vec(12*(7 + 37*x - 15*x^2 + 3*x^3) / (1 - x)^5 + O(x^50)) \\ Michel Marcus, Mar 29 2015 (PARI) vector(50, n, n--; (2*n+1)*(2*n+2)*(2*n+6)*(2*n+7)) \\ Michel Marcus, Mar 29 2015 CROSSREFS Sequence in context: A220016 A219827 A219719 * A219577 A093284 A027794 Adjacent sequences: A069077 A069078 A069079 * A069081 A069082 A069083 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Apr 05 2002 STATUS approved

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Last modified April 21 01:34 EDT 2024. Contains 371850 sequences. (Running on oeis4.)