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 1-2 of 2 results.

A146541 Binomial transform of A010688.

Original entry on oeis.org

1, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592
Offset: 0

Views

Author

Philippe Deléham, Oct 31 2008

Keywords

Comments

Hankel transform is := 1,-48,0,0,0,0,0,0,0,...

Links

Crossrefs

Cf. A000007, A011782, A000079, A003945, A046055, A146523, A082505, A135092.
Essentially the same as A132479, A077552, A020707.

Programs

  • Mathematica
    Join[{1},2^Range[3,40]] (* Harvey P. Dale, Feb 28 2016 *)
  • PARI
    Vec((1+6*x)/(1-2*x) + O(x^50)) \\ Colin Barker, Mar 17 2016

Formula

a(0)=1, a(n) = 2^(n+2) for n>0.
a(n) = Sum_{k, 0..n} A109466(n,k)*A146534(k).
a(n) = A132479(n), n>1. - R. J. Mathar, Nov 02 2008
G.f.: (1+6*x) / (1-2*x). - Colin Barker, Mar 17 2016

Extensions

Corrected and extended by Harvey P. Dale, Feb 28 2016

A240530 a(n) = 4*(2*n)! / (n!)^2.

Original entry on oeis.org

4, 8, 24, 80, 280, 1008, 3696, 13728, 51480, 194480, 739024, 2821728, 10816624, 41602400, 160466400, 620470080, 2404321560, 9334424880, 36300541200, 141381055200, 551386115280, 2153031497760, 8416395854880, 32933722910400, 128990414732400
Offset: 0

Views

Author

Vincenzo Librandi, Apr 12 2014

Keywords

Comments

Apart from first term, the same as A146534. - Arkadiusz Wesolowski, Apr 12 2014

Links

Crossrefs

Cf. A000984, A028329, A146534.

Programs

  • GAP
    List([0..30], n-> 4*Binomial(2*n,n) ); # G. C. Greubel, Dec 19 2019
  • Magma
    [4*Binomial (2*n,n): n in [0..30]];
  • Maple
    seq( 4*binomial(2*n,n), n=0..30); # G. C. Greubel, Dec 19 2019
  • Mathematica
    Table[4*(2*n)!/(n!)^2, {n, 0, 40}] (* or *) CoefficientList[Series[4/Sqrt[1 - 4 x], {x, 0, 50}], x]
  • PARI
    vector(31, n, 4*binomial(2*n-2, n-1)) \\ G. C. Greubel, Dec 19 2019
  • Sage
    [4*binomial(2*n,n) for n in (0..30)] # G. C. Greubel, Dec 19 2019

Formula

G.f.: 4/sqrt(1-4*x).
a(n) = 4*binomial(2*n, n) = 4*A000984(n) = 2*A028329(n).
D-finite with recurrence: n*a(n) - 2*(2*n-1)*a(n-1) = 0 for n > 0.
Showing 1-2 of 2 results.

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