OFFSET
0,3
COMMENTS
The sixth column of the triangle A107711.
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = A107711(n+5,5) = binomial(n+5,5)*gcd(n,5)/(n+5), with n >= 0.
O.g.f.: ((1+x^20) + x*(1+x^18) + 3*x^2*(1+x^16) + 7*x^3*(1+x^14) + 14*x^4*(1+x^12) + 121*x^5*(1+x^10)+37*x^6*(1+x^8) + 51*x^7*(1+x^6) + 64*x^8*(1+x^4) + 73*x^9*(1+x^2) + 381*x^10)/(1-x^5)^5. From the 5-section using n = 5*k + j, for j = 0, 1, 2, 3, 4.
Sum_{n>=0} 1/a(n) = 20/3 - 16*sqrt(10-22/sqrt(5))*Pi/5. - Amiram Eldar, Sep 20 2022
MATHEMATICA
a[n_] := Binomial[n + 4, 4] * GCD[n, 5]/5; Table[a[n], {n, 0, 40}] (* Amiram Eldar, Sep 20 2022 *)
PROG
(PARI) a(n) = binomial(n+4, 4)*gcd(n, 5)/5 \\ Charles R Greathouse IV, Feb 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 24 2014
STATUS
approved