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.

A382650 Expansion of 1/(1 - x*(1 + 4*x)^(3/2))^3.

Original entry on oeis.org

1, 3, 24, 100, 471, 2043, 8422, 34818, 137649, 543655, 2096508, 8031948, 30355155, 113929497, 423562614, 1565841650, 5745557853, 20989365057, 76206968356, 275721399480, 992423144247, 3562075121911, 12728422443654, 45379998032202, 161158522838105, 571293893581389
Offset: 0

Views

Author

Seiichi Manyama, Apr 02 2025

Keywords

Comments

a(100) is negative.

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, 4^(n-k)*binomial(k+2, 2)*binomial(3*k/2, n-k));

Formula

a(n) = Sum_{k=0..n} 4^(n-k) * binomial(k+2,2) * binomial(3*k/2,n-k).

A382647 Expansion of 1/(1 - x*(1 + 4*x)^(1/2))^2.

Original entry on oeis.org

1, 2, 7, 12, 37, 50, 187, 128, 1057, -502, 7679, -14420, 73453, -212554, 843019, -2848064, 10602409, -37875706, 139533151, -510006524, 1885309253, -6974175142, 25940881947, -96731191728, 361980829841, -1358121976978, 5109416286295, -19267391982612
Offset: 0

Views

Author

Seiichi Manyama, Apr 02 2025

Keywords

Crossrefs

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(1/2))^2)); // Vincenzo Librandi, May 13 2025
  • Mathematica
    Table[Sum[4^(n-k)* (k+1)* Binomial[k/2, n-k],{k,0,n}],{n,0,28}] (* Vincenzo Librandi, May 13 2025 *)
  • PARI
    a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(k/2, n-k));
    

Formula

a(n) = Sum_{k=0..n} 4^(n-k) * (k+1) * binomial(k/2,n-k).
Showing 1-2 of 2 results.