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

37,2

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).

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A161651 A162166 A162392 * A004420 A020930 A104761

Adjacent sequences: A010987 A010988 A010989 * A010991 A010992 A010993

Keyword

nonn

Author

N. J. A. Sloane

Status

approved