A060541 a(n) = binomial(4*n, 4).

1, 70, 495, 1820, 4845, 10626, 20475, 35960, 58905, 91390, 135751, 194580, 270725, 367290, 487635, 635376, 814385, 1028790, 1282975, 1581580, 1929501, 2331890, 2794155, 3321960, 3921225, 4598126, 5359095, 6210820, 7160245, 8214570, 9381251, 10668000, 12082785

Offset: 1

Author

Henry Bottomley, Apr 02 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000027, A000332, A000384, A006566, A015219, A060539.

Programs

Magma

[Binomial(4 n, 4): n in [1..40]]; // Vincenzo Librandi, Jan 20 2015

Mathematica

Table[Binomial[4n, 4], {n, 100}] (* Wesley Ivan Hurt, Sep 27 2013 *)
LinearRecurrence[{5,-10,10,-5,1},{1,70,495,1820,4845},40] (* Harvey P. Dale, Jan 13 2015 *)

PARI

a(n) = n*(2*n - 1)*(4*n - 1)*(4*n - 3)/3; \\ Harry J. Smith, Jul 06 2009

Formula

a(n) = n*(2n-1)*(4n-1)*(4n-3)/3.

a(n) = n * A015219(n-1) = A000332(4n) = A060539(n, 4).

G.f.: x*(1+65*x+155*x^2+35*x^3) / (1-x)^5. - R. J. Mathar, Oct 03 2011

From Amiram Eldar, Mar 08 2022: (Start)

Sum_{n>=1} 1/a(n) = 6*log(2) - Pi.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*sqrt(2)*log(sqrt(2)-1) - log(2) + (2*sqrt(2) - 3/2)*Pi. (End)

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Jul 06 2009