OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Richard P. Brent, Generalising Tuenter's binomial sums, arXiv:1407.3533 [math.CO], 2014. (page 16)
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
O.g.f.: (-555731 + 3334387*x - 8306446*x^2 + 12594614*x^3 - 1244143*x^4 + 8922919*x^5)/(1-x)^6.
E.g.f.: (-555731 + 555732*x - 263104*x^2 + 354048*x^3 + 399360*x^4 + 122880*x^5)*exp(x).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
n*a(n) = 1 + 3^11*(n-1)/(n+1) + 5^11*((n-1)*(n-2))/((n+1)*(n+2)) + ... for n >= 1. See A245244. - Peter Bala, Jan 19 2019
MAPLE
[122880*n^5-829440*n^4+2258688*n^3-3076288*n^2+2079892*n-555731$n=0..30]; # Muniru A Asiru, Jan 28 2019
MATHEMATICA
Table[122880 n^5 - 829440 n^4 + 2258688 n^3 - 3076288 n^2 + 2079892 n - 555731, {n, 0, 40}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {-555731, 1, 29525, 1657129, 16591741, 80872529}, 30] (* Harvey P. Dale, Feb 10 2021 *)
PROG
(Magma) [122880*n^5 - 829440*n^4 + 2258688*n^3 -3076288*n^2 + 2079892*n - 555731: n in [0..30]];
(PARI) lista(nn) = for(n=0, nn, print1(122880*n^5 - 829440*n^4 + 2258688*n^3 - 3076288*n^2 + 2079892*n - 555731, ", ")); \\ Altug Alkan, Apr 26 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Vincenzo Librandi, Apr 26 2016
STATUS
approved