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

1,2

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).

Formula

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

a(n) = n*A015219(n-1) = A000332(4*n) = 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)

From Elmo R. Oliveira, Nov 28 2025: (Start)

E.g.f.: exp(x)*x*(3 + 102*x + 144*x^2 + 32*x^3)/3.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

a(n) = A054777(n)/24. (End)

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 *)

Prog

(PARI) a(n) = n*(2*n - 1)*(4*n - 1)*(4*n - 3)/3; \\ Harry J. Smith, Jul 06 2009
(Magma) [Binomial(4*n, 4): n in [1..40]]; // Vincenzo Librandi, Jan 20 2015

Crossrefs

Cf. A000027, A000332, A000384, A006566, A015219, A054777, A060539.

Sequence in context: A154085 A220365 A007330 * A235302 A229576 A234556

Adjacent sequences: A060538 A060539 A060540 * A060542 A060543 A060544

Keyword

nonn,easy

Author

Henry Bottomley, Apr 02 2001

Extensions

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

Status

approved