A017769 Binomial coefficients C(53,n).

1, 53, 1378, 23426, 292825, 2869685, 22957480, 154143080, 886322710, 4431613550, 19499099620, 76223753060, 266783135710, 841392966470, 2403979904200, 6250347750920, 14844575908435, 32308782859535, 64617565719070, 119032357903550, 202355008436035

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full
• easy

Comments

Row 53 of A007318.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..53 (full sequence)

Crossrefs

Cf. A010926-A011001, A017765-A017768, A017770-A017816.

Programs

Magma

[Binomial(53,n): n in [0..53]]; // G. C. Greubel, Nov 13 2018

Maple

seq(binomial(53,n), n=0..53); # Nathaniel Johnston, Jun 24 2011

Mathematica

With[{k = 53}, Array[Binomial[k, #] &, k + 1, 0]] (* Michael De Vlieger, Jul 06 2018 *)
With[{nmax = 53}, CoefficientList[Series[Hypergeometric1F1[-53, 1, -x], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Nov 13 2018 *)

PARI

vector(53, n, n--; binomial(53,n)) \\ G. C. Greubel, Nov 13 2018

Sage

[binomial(53, n) for n in range(54)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 13 2018: (Start)

G.f.: (1+x)^53.

E.g.f.: 1F1(-53; 1; -x), where 1F1 is the confluent hypergeometric function. (End)