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

44,2

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A010995, A010996, A001787, A242091.

Sequence in context: A161690 A162183 A162418 * A163721 A292209 A317895

Adjacent sequences: A010994 A010995 A010996 * A010998 A010999 A011000

Keyword

nonn

Author

N. J. A. Sloane

Status

approved