A010997 a(n) = binomial coefficient C(n,44).

1, 45, 1035, 16215, 194580, 1906884, 15890700, 115775100, 752538150, 4431613550, 23930713170, 119653565850, 558383307300, 2448296039700, 10142940735900, 39895566894540, 149608375854525, 536830054536825, 1849081298960175, 6131164307078475, 19619725782651120

Offset: 44

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 44..1000
• Index entries for linear recurrences with constant coefficients, signature (45, -990, 14190, -148995, 1221759, -8145060, 45379620, -215553195, 886163135, -3190187286, 10150595910, -28760021745, 73006209045, -166871334960, 344867425584, -646626422970, 1103068603890, -1715884494940, 2438362177020, -3169870830126, 3773655750150, -4116715363800, 4116715363800, -3773655750150, 3169870830126, -2438362177020, 1715884494940, -1103068603890, 646626422970, -344867425584, 166871334960, -73006209045, 28760021745, -10150595910, 3190187286, -886163135, 215553195, -45379620, 8145060, -1221759, 148995, -14190, 990, -45, 1).

Crossrefs

Cf. A010995, A010996, A001787, A242091.

Programs

Magma

[Binomial(n, 44): n in [44..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,44),n=44..67); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n,44],{n,44,70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Formula

G.f.: x^44/(1-x)^45. - Zerinvary Lajos, Dec 20 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=44} 1/a(n) = 44/43.

Sum_{n>=44} (-1)^n/a(n) = A001787(44)*log(2) - A242091(44)/43! = 387028092977152*log(2) - 7178888410874815560070307159852/26760193632961425 = 0.9786869603... (End)