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 A264891 a(n) = n*(5*n - 3)*(25*n^2 - 15*n - 6)/8. 2
 0, 1, 112, 783, 2839, 7480, 16281, 31192, 54538, 89019, 137710, 204061, 291897, 405418, 549199, 728190, 947716, 1213477, 1531548, 1908379, 2350795, 2865996, 3461557, 4145428, 4925934, 5811775, 6812026, 7936137, 9193933, 10595614, 12151755, 13873306 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Doubly heptagonal numbers. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1200 OEIS Wiki, Figurate numbers Eric Weisstein's World of Mathematics, Heptagonal Number Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1) FORMULA G.f.: x*(1 + 107*x + 233*x^2 + 34*x^3)/(1 - x)^5. a(n) = A000566(A000566(n)). a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Nov 28 2015 Sum_{n>0} 1/a(n) = (4*(sqrt(33)*gamma + sqrt(33)*polygamma(0, 2/5) - 3*polygamma(0, (1/10)*(7 - sqrt(33))) + 3 polygamma(0, (1/10)* (7 + sqrt(33)))))/(9*sqrt(33)) = 1.0108420043...., where gamma is the Euler-Mascheroni constant (A001620), and polygamma is the derivative of the logarithm of the gamma function. E.g.f.: x*(8 + 440*x + 600*x^2 + 125*x^3)*exp(x)/8, - Robert Israel, Dec 02 2015 MAPLE seq(n*(5*n - 3)*(25*n^2 - 15*n - 6)/8, n=0..100); # Robert Israel, Dec 02 2015 MATHEMATICA Table[n (5 n - 3) (25 n^2 - 15 n - 6)/8, {n, 0, 35}] LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 112, 783, 2839}, 40] (* Harvey P. Dale, Nov 19 2019 *) PROG (PARI) vector(100, n, n--; n*(5*n-3)*(25*n^2-15*n-6)/8) \\ Altug Alkan, Nov 27 2015 (Magma) [n*(5*n-3)*(25*n^2-15*n-6)/8: n in [0..30]]; // Vincenzo Librandi, Nov 28 2015 CROSSREFS Cf. A000566, A002817, A000583, A232713, A063249. Sequence in context: A154063 A205250 A047631 * A203796 A203789 A211448 Adjacent sequences: A264888 A264889 A264890 * A264892 A264893 A264894 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Nov 27 2015 STATUS approved

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Last modified March 25 22:40 EDT 2023. Contains 361529 sequences. (Running on oeis4.)