A010991 Binomial coefficient C(n,38).

1, 39, 780, 10660, 111930, 962598, 7059052, 45379620, 260932815, 1362649145, 6540715896, 29135916264, 121399651100, 476260169700, 1768966344600, 6250347750920, 21094923659355, 68248282427325, 212327989773900, 636983969321700, 1847253511032930, 5189902721473470

Offset: 38

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 38..1000
• Index entries for linear recurrences with constant coefficients, signature (39, -741, 9139, -82251, 575757, -3262623, 15380937, -61523748, 211915132, -635745396, 1676056044, -3910797436, 8122425444, -15084504396, 25140840660, -37711260990, 51021117810, -62359143990, 68923264410, -68923264410, 62359143990, -51021117810, 37711260990, -25140840660, 15084504396, -8122425444, 3910797436, -1676056044, 635745396, -211915132, 61523748, -15380937, 3262623, -575757, 82251, -9139, 741, -39, 1).

Crossrefs

Cf. A010988, A010989, A010990, A001787, A242091.

Programs

Magma

[Binomial(n, 38): n in [38..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,38),n=38..57); # Zerinvary Lajos, Dec 19 2008

Mathematica

Table[Binomial[n,38],{n,38,66}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

Formula

G.f.: x^38/(1-x)^39. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=38} 1/a(n) = 38/37.

Sum_{n>=38} (-1)^n/a(n) = A001787(38)*log(2) - A242091(38)/37! = 5222680231936*log(2) - 31812289115113208816827133/8787716212275 = 0.9755552351... (End)