A010977 a(n) = binomial coefficient C(n,24).

1, 25, 325, 2925, 20475, 118755, 593775, 2629575, 10518300, 38567100, 131128140, 417225900, 1251677700, 3562467300, 9669554100, 25140840660, 62852101650, 151584480450, 353697121050, 800472431850, 1761039350070, 3773655750150, 7890371113950, 16123801841550

Offset: 24

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 24..1000
• Index entries for linear recurrences with constant coefficients, signature (25, -300, 2300, -12650, 53130, -177100, 480700, -1081575, 2042975, -3268760, 4457400, -5200300, 5200300, -4457400, 3268760, -2042975, 1081575, -480700, 177100, -53130, 12650, -2300, 300, -25, 1).

Crossrefs

Pascal's triangle A007318 diagonal. - Zerinvary Lajos, Aug 04 2008

Cf. A010970, A010971, A010972, A001787, A242091.

Programs

Magma

[ Binomial(n,24): n in [24..90]]; // Vincenzo Librandi, Mar 26 2011

Maple

seq(binomial(n,24),n=24..41); # Zerinvary Lajos, Aug 04 2008

Mathematica

Table[Binomial[n,24],{n,24,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

PARI

x='x+O('x^50); Vec(x^24/(1-x)^25) \\ G. C. Greubel, Nov 23 2017

Formula

G.f.: x^24/(1-x)^25. - Zerinvary Lajos, Aug 04 2008 [Corrected by Georg Fischer, May 19 2019]

a(n) = n/(n-24) * a(n-1), n > 24. - Vincenzo Librandi, Mar 26 2011

From Amiram Eldar, Dec 11 2020: (Start)

Sum_{n>=24} 1/a(n) = 24/23.

Sum_{n>=24} (-1)^n/a(n) = A001787(24)*log(2) - A242091(24)/23! = 201326592*log(2) - 15566188845789952/111546435 = 0.9627768409... (End)