A264894 a(n) = n*(7*n - 5)*(49*n^2 - 35*n - 10)/8.

0, 1, 261, 1956, 7291, 19500, 42846, 82621, 145146, 237771, 368875, 547866, 785181, 1092286, 1481676, 1966875, 2562436, 3283941, 4148001, 5172256, 6375375, 7777056, 9398026, 11260041, 13385886, 15799375, 18525351, 21589686, 25019281, 28842066, 33087000

Offset: 0

Author

Ilya Gutkovskiy, Nov 27 2015

Keywords

• nonn
• easy

Comments

Doubly 9-gonal (or nonagonal) numbers.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• OEIS Wiki, Figurate numbers
• Eric Weisstein's World of Mathematics, Nonagonal Number
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)

Crossrefs

Cf. A001106, A002817, A000583, A232713, A063249.

Programs

Magma

[n*(7*n-5)*(49*n^2-35*n-10)/8: n in [0..30]]; // Vincenzo Librandi, Nov 28 2015

Mathematica

Table[n (7 n - 5) (49 n^2 - 35 n - 10)/8, {n, 0, 30}]
LinearRecurrence[{5,-10,10,-5,1},{0,1,261,1956,7291},40] (* Harvey P. Dale, Apr 29 2017 *)

PARI

vector(100, n, n--; n*(7*n-5)*(49*n^2-35*n-10)/8) \\ Altug Alkan, Nov 27 2015

Formula

G.f.: x*(1 + 256*x + 661*x^2 + 111*x^3)/(1 - x)^5.

a(n) = A001106(A001106(n)).

Sum_{n>0} 1/a(n) = (4*(sqrt(65)*gamma + sqrt(65)*polygamma(0, 2/7) - 5*polygamma(0, (1/14)*(9 - sqrt(65))) + 5*polygamma(0, (1/14)*(9 + sqrt(65)))))/(25*sqrt(65)) = 1.0045877861645573..., where gamma is the Euler-Mascheroni constant (A001620), and polygamma is the derivative of the logarithm of the gamma function.