A011001 Binomial coefficient C(n,48).

1, 49, 1225, 20825, 270725, 2869685, 25827165, 202927725, 1420494075, 8996462475, 52179482355, 279871768995, 1399358844975, 6566222272575, 29078984349975, 122131734269895, 488526937079580, 1867897112363100, 6848956078664700, 24151581961607100

Offset: 48

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 48..1000
• Index entries for linear recurrences with constant coefficients, signature (49, -1176, 18424, -211876, 1906884, -13983816, 85900584, -450978066, 2054455634, -8217822536, 29135916264, -92263734836, 262596783764, -675248872536, 1575580702584, -3348108992991, 6499270398159, -11554258485616, 18851684897584, -28277527346376, 39049918716424, -49699896548176, 58343356817424, -63205303218876, 63205303218876, -58343356817424, 49699896548176, -39049918716424, 28277527346376, -18851684897584, 11554258485616, -6499270398159, 3348108992991, -1575580702584, 675248872536, -262596783764, 92263734836, -29135916264, 8217822536, -2054455634, 450978066, -85900584, 13983816, -1906884, 211876, -18424, 1176, -49, 1).

Crossrefs

Cf. A010999, A011000, A001787, A242091.

Programs

Magma

[Binomial(n, 48): n in [48..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,48),n=48..67); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n,48],{n,48,77}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

PARI

a(n)=binomial(n,48)  \\ Charles R Greathouse IV, Jan 08 2013

Python

A011001_list, m = [], [1]*49
for _ in range(10**2):
    A011001_list.append(m[-1])
    for i in range(48):
        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

Formula

G.f.: x^48/(1-x)^49. - Zerinvary Lajos, Dec 20 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=48} 1/a(n) = 48/47.

Sum_{n>=48} (-1)^n/a(n) = A001787(48)*log(2) - A242091(48)/47! = 6755399441055744*log(2) - 21594096339911519462651644572315136 / 4611673369413685575 = 0.9803635237... (End)