A010984 Binomial coefficient C(n,31).

1, 32, 528, 5984, 52360, 376992, 2324784, 12620256, 61523748, 273438880, 1121099408, 4280561376, 15338678264, 51915526432, 166871334960, 511738760544, 1503232609098, 4244421484512, 11554258485616, 30405943383200, 77535155627160, 191991813933920

Offset

31,2

Links

T. D. Noe, Table of n, a(n) for n = 31..1000

Index entries for linear recurrences with constant coefficients, signature (32, -496, 4960, -35960, 201376, -906192, 3365856, -10518300, 28048800, -64512240, 129024480, -225792840, 347373600, -471435600, 565722720, -601080390, 565722720, -471435600, 347373600, -225792840, 129024480, -64512240, 28048800, -10518300, 3365856, -906192, 201376, -35960, 4960, -496, 32, -1).

Formula

G.f.: x^31/(1-x)^32. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 21 2017

From Amiram Eldar, Dec 12 2020: (Start)

Sum_{n>=31} 1/a(n) = 31/30.

Sum_{n>=31} (-1)^(n+1)/a(n) = A001787(31)*log(2) - A242091(31)/30! = 33285996544*log(2) - 6717121856795533085173/291136195350 = 0.9704936372... (End)

Maple

seq(binomial(n, 31), n=31..53); # Zerinvary Lajos, Dec 19 2008

Mathematica

Table[Binomial[n, 31], {n, 31, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

Prog

(Magma) [Binomial(n, 31): n in [31..70]]; // Vincenzo Librandi, Jun 12 2013
(PARI) x='x+O('x^50); Vec(x^31/(1-x)^32) \\ G. C. Greubel, Nov 23 2017

Crossrefs

Cf. A010980, A010981, A010982, A001787, A242091

Sequence in context: A161987 A162379 A162739 * A022596 A130609 A154306

Adjacent sequences: A010981 A010982 A010983 * A010985 A010986 A010987

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved