A151989 a(n) = A001512(n)/24 = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)/24.

1, 126, 1001, 3876, 10626, 23751, 46376, 82251, 135751, 211876, 316251, 455126, 635376, 864501, 1150626, 1502501, 1929501, 2441626, 3049501, 3764376, 4598126, 5563251, 6672876, 7940751, 9381251, 11009376, 12840751, 14891626, 17178876, 19720001, 22533126

Offset: 0

Author

M. F. Hasler, Sep 14 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A001512.

Programs

Magma

[(5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)/24: n in [0..30]]; // Vincenzo Librandi, Aug 17 2011

Mathematica

(Times@@#)/24&/@Table[5n+i,{n,0,35},{i,4}] (* Harvey P. Dale, Aug 16 2011 *)
Table[Binomial[5*n+4,4], {n,0,30}] (* G. C. Greubel, Nov 08 2018 *)

PARI

vector(30, n, n--; binomial(5*n+4,4)) \\ G. C. Greubel, Nov 08 2018

Formula

Sum_{k>=0} 1/a(k) = 4*sqrt(10-22/sqrt(5))*Pi/5. - Jaume Oliver Lafont, May 22 2010

G.f.: (1 + 121*x + 381*x^2 + 121*x^3 + x^4)/(1-x)^5. - Colin Barker, Aug 17 2012

Sum_{n>=0} (-1)^n/a(n) = 32*log(2)/5 - 8*arccoth(3/sqrt(5))/sqrt(5). - Amiram Eldar, Sep 20 2022