cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A002761 Number of ways of getting a royal flush, other straight flush, 4 of a kind, full house, other flush, other straight, 3 of a kind, 2 pair, a pair or nothing in 5-card poker.

Original entry on oeis.org

4, 36, 624, 3744, 5108, 10200, 54912, 123552, 1098240, 1302540
Offset: 1

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Author

N. J. A. Sloane, Koreen M Mielke (mielkk72(AT)VAXA.CIS.UWOSH.EDU)

Keywords

References

  • J. Scarne, Scarne's Complete Guide to Gambling, Simon and Schuster, 1961, p. 582.

Crossrefs

Formula

From Jianing Song, Apr 06 2019: (Start)
a(n) = A002806(11-n) for 1 <= n <= 10.
Sum_{i=1..10} a(i) = binomial(52,5) = A017768(5). (End)

A002806 Number of ways of getting nothing, a pair, 2 pair, 3 of a kind, other straight, other flush, full house, 4 of a kind, other straight flush, or a royal flush in 5-card poker.

Original entry on oeis.org

1302540, 1098240, 123552, 54912, 10200, 5108, 3744, 624, 36, 4
Offset: 1

Views

Author

N. J. A. Sloane, Koreen M Mielke (mielkk72(AT)VAXA.CIS.UWOSH.EDU)

Keywords

References

  • J. Scarne, Scarne's Complete Guide to Gambling, Simon and Schuster, 1961, p. 582.

Crossrefs

Cf. A002761.

Formula

From Jianing Song, Apr 06 2019: (Start)
a(n) = A002761(11-n) for 1 <= n <= 10.
Sum_{i=1..10} a(i) = binomial(52,5) = A017768(5). (End)

A017769 Binomial coefficients C(53,n).

Original entry on oeis.org

1, 53, 1378, 23426, 292825, 2869685, 22957480, 154143080, 886322710, 4431613550, 19499099620, 76223753060, 266783135710, 841392966470, 2403979904200, 6250347750920, 14844575908435, 32308782859535, 64617565719070, 119032357903550, 202355008436035
Offset: 0

Views

Author

Keywords

Comments

Row 53 of A007318.

Crossrefs

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)
Showing 1-3 of 3 results.