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) = 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
KEYWORD
nonn,easy,changed
AUTHOR
Ilya Gutkovskiy, Nov 27 2015
STATUS
approved