A010985 Binomial coefficient C(n,32).

1, 33, 561, 6545, 58905, 435897, 2760681, 15380937, 76904685, 350343565, 1471442973, 5752004349, 21090682613, 73006209045, 239877544005, 751616304549, 2254848913647, 6499270398159, 18053528883775, 48459472266975, 125994627894135, 317986441828055

Offset: 32

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 32..1000
• Index entries for linear recurrences with constant coefficients, signature (33, -528, 5456, -40920, 237336, -1107568, 4272048, -13884156, 38567100, -92561040, 193536720, -354817320, 573166440, -818809200, 1037158320, -1166803110, 1166803110, -1037158320, 818809200, -573166440, 354817320, -193536720, 92561040, -38567100, 13884156, -4272048, 1107568, -237336, 40920, -5456, 528, -33, 1).

Crossrefs

Cf. A010982, A010984, A001787, A242091.

Programs

Magma

[Binomial(n, 32): n in [32..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,32),n=32..55); # Zerinvary Lajos, Dec 19 2008

Mathematica

Table[Binomial[n,32],{n,32,60}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

PARI

x='x+O('x^50); Vec(x^32/(1-x)^33) \\ G. C. Greubel, Nov 23 2017

Formula

G.f.: x^32/(1-x)^33. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 21 2017

From Amiram Eldar, Dec 12 2020: (Start)

Sum_{n>=32} 1/a(n) = 32/31.

Sum_{n>=32} (-1)^n/a(n) = A001787(32)*log(2) - A242091(32)/31! = 68719476736*log(2) - 214947899422115237851136/4512611027925 = 0.9713417027... (End)