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.

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A228647 a(n) = A001609(n^2) for n>=1, where g.f. of A001609 is x*(1+3*x^2)/(1-x-x^3).

Original entry on oeis.org

1, 5, 31, 453, 14131, 946781, 136250983, 42115660581, 27961563559891, 39874307297033165, 122134599693975367423, 803522677430288749340325, 11354589189995520431547851761, 344634362031276605039944979868611, 22467750416780812361715214948922598721, 3146114090698891414621617889648190060326821
Offset: 1

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Author

Paul D. Hanna, Aug 28 2013

Keywords

Comments

A001609 forms the logarithmic derivative of Narayana's cows sequence A000930.

Examples

			L.g.f.: L(x) = x + 5*x^2/2 + 31*x^3/3 + 453*x^4/4 + 14131*x^5/5 +...
where
exp(L(x)) = 1 + x + 3*x^2 + 13*x^3 + 128*x^4 + 2974*x^5 + 161048*x^6 + 19632276*x^7 +...+ A228648(n)*x^n +...
		

Crossrefs

Programs

  • PARI
    {A001609(n)=n*polcoeff(-log(1-x-x^3 +x*O(x^n)), n)}
    {a(n)=A001609(n^2)}
    for(n=1,20,print1(a(n),", "))

Formula

Equals the logarithmic derivative of A228648.

A231621 a(n) = A000930(n*(n+1)/2), where A000930 is Narayana's cows sequence.

Original entry on oeis.org

1, 1, 2, 6, 28, 189, 1873, 27201, 578949, 18059374, 825604416, 55315679788, 5431645680297, 781666575692345, 164861247948842305, 50959194632488457965, 23085190353310504913320, 15326793132326730009566200, 14913379277290330452859885202, 21267074956884103635776195255433, 44447403127130268192387935737712641
Offset: 0

Views

Author

Paul D. Hanna, Nov 13 2013

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[1/(1 - x - x^3), {x, 0, n*(n + 1)/2}], {n,0,50}] (* G. C. Greubel, Apr 26 2017 *)
  • PARI
    {a(n) = polcoeff(1/(1-x-x^3 + x*O(x^(n*(n+1)/2))), n*(n+1)/2)}
    for(n=0, 20, print1(a(n), ", "))

Formula

a(n) = [x^(n*(n+1)/2)] 1 / (1 - x - x^3) for n>=0.
Showing 1-2 of 2 results.