A011000 a(n) = binomial coefficient C(n,47).

1, 48, 1176, 19600, 249900, 2598960, 22957480, 177100560, 1217566350, 7575968400, 43183019880, 227692286640, 1119487075980, 5166863427600, 22512762077400, 93052749919920, 366395202809685, 1379370175283520, 4981058966301600, 17302625882942400, 57963796707857040

Offset: 47

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 47..1000
• Index entries for linear recurrences with constant coefficients, signature (48, -1128, 17296, -194580, 1712304, -12271512, 73629072, -377348994, 1677106640, -6540715896, 22595200368, -69668534468, 192928249296, -482320623240, 1093260079344, -2254848913647, 4244421484512, -7309837001104, 11541847896480, -16735679449896, 22314239266528, -27385657281648, 30957699535776, -32247603683100, 30957699535776, -27385657281648, 22314239266528, -16735679449896, 11541847896480, -7309837001104, 4244421484512, -2254848913647, 1093260079344, -482320623240, 192928249296, -69668534468, 22595200368, -6540715896, 1677106640, -377348994, 73629072, -12271512, 1712304, -194580, 17296, -1128, 48, -1).

Crossrefs

Cf. A010998, A010999, A001787, A242091.

Programs

Magma

[Binomial(n, 47): n in [47..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,47),n=47..67); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n,47],{n,47,77}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Formula

G.f.: x^47/(1-x)^48. - Zerinvary Lajos, Dec 20 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=47} 1/a(n) = 47/46.

Sum_{n>=47} (-1)^(n+1)/a(n) = A001787(47)*log(2) - A242091(47)/46! = 3307330976350208*log(2) - 1349631021244469672053597823194021/588724259925151350 = 0.9799696418... (End)