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A264891
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a(n) = n*(5*n - 3)*(25*n^2 - 15*n - 6)/8.
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2
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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
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OFFSET
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0,3
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COMMENTS
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Doubly heptagonal numbers.
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LINKS
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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)
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FORMULA
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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
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MAPLE
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seq(n*(5*n - 3)*(25*n^2 - 15*n - 6)/8, n=0..100); # Robert Israel, Dec 02 2015
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A000566, A002817, A000583, A232713, A063249.
Sequence in context: A154063 A205250 A047631 * A203796 A203789 A211448
Adjacent sequences: A264888 A264889 A264890 * A264892 A264893 A264894
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KEYWORD
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nonn,easy
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AUTHOR
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Ilya Gutkovskiy, Nov 27 2015
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STATUS
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approved
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