A010990 Binomial coefficient C(n,37).

1, 38, 741, 9880, 101270, 850668, 6096454, 38320568, 215553195, 1101716330, 5178066751, 22595200368, 92263734836, 354860518600, 1292706174900, 4481381406320, 14844575908435, 47153358767970, 144079707346575, 424655979547800, 1210269541711230, 3342649210440540

Offset: 37

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 37..1000
• Index entries for linear recurrences with constant coefficients, signature (38, -703, 8436, -73815, 501942, -2760681, 12620256, -48903492, 163011640, -472733756, 1203322288, -2707475148, 5414950296, -9669554100, 15471286560, -22239974430, 28781143380, -33578000610, 35345263800, -33578000610, 28781143380, -22239974430, 15471286560, -9669554100, 5414950296, -2707475148, 1203322288, -472733756, 163011640, -48903492, 12620256, -2760681, 501942, -73815, 8436, -703, 38, -1).

Crossrefs

Cf. A010987, A010988, A010989, A001787, A242091.

Programs

Magma

[Binomial(n, 37): n in [37..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,37),n=37..55); # Zerinvary Lajos, Dec 19 2008

Mathematica

Table[Binomial[n,37],{n,37,66}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

Formula

G.f.: x^37/(1-x)^38. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=37} 1/a(n) = 37/36.

Sum_{n>=37} (-1)^(n+1)/a(n) = A001787(37)*log(2) - A242091(37)/36! = 2542620639232*log(2) - 31812289115104183594771283/18050444111700 = 0.9749413644... (End)