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.

A246575 Expansion of (Product_{r>=1} (1-x^r))*x^(k^2) / Product_{i=1..k} (1-x^i)^2 with k=1.

Original entry on oeis.org

0, 1, 1, 0, -1, -2, -2, -2, -1, 0, 1, 2, 3, 3, 3, 3, 2, 1, 0, -1, -2, -3, -4, -4, -4, -4, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -6, -6, -6, -6, -6, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 5, 4, 3
Offset: 0

Views

Author

N. J. A. Sloane, Aug 31 2014

Keywords

Links

Crossrefs

k=0 gives A010815.
Cf. A246575, A246576, A246577, A246578, A078616.

Programs

  • Maple
    fGL:=proc(k) local a,i,r;
a:=x^(k^2)/mul((1-x^i)^2,i=1..k);
a:=a*mul(1-x^r,r=1..101);
series(a,x,101);
seriestolist(%);
end;fGL(1);
  • Mathematica
    nmax = 100; CoefficientList[Series[x*Exp[Sum[x^k/k * (1 - 2*x^k)/(1 - x^k), {k, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 17 2015 *)
  • PARI
    {a(n) = my(A=1); A = x*exp( sum(k=1, n+1, x^k/k * (1-2*x^k)/(1 - x^k) +x*O(x^n) ) ); polcoeff(A, n)}
for(n=0, 100, print1(a(n), ", ")) \\ Paul D. Hanna, Dec 14 2015

Formula

G.f.: x*exp( Sum_{n>=1} x^n/n * (1 - 2*x^n)/(1 - x^n) ). - Paul D. Hanna, Dec 14 2015

A246576 G.f.: (Product_{r>=1} (1 - x^r))*x^(k^2)/Product_{i=1..k} ((1 - x^i)^2) with k=2.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 1, 1, -1, -2, -4, -5, -6, -6, -5, -4, -1, 1, 5, 7, 11, 12, 15, 14, 15, 12, 11, 6, 3, -3, -7, -13, -17, -22, -25, -28, -29, -29, -28, -25, -22, -16, -11, -3, 3, 12, 18, 27, 32, 40, 43, 49, 49, 52, 49, 49, 43, 40, 31, 25, 14, 6, -6, -15, -27, -36, -47, -55, -64
Offset: 0

Views

Author

N. J. A. Sloane, Aug 31 2014

Keywords

References

  • Fulman, Jason. Random matrix theory over finite fields. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 51--85. MR1864086 (2002i:60012). See top of page 70.

Crossrefs

k=0 gives A010815. Cf. A246575-A246578.

Programs

  • Maple
    fGL:=proc(k) local a,i,r;
a:=x^(k^2)/mul((1-x^i)^2,i=1..k);
a:=a*mul(1-x^r,r=1..101);
series(a,x,101);
seriestolist(%);
end;fGL(2);

A246577 G.f.: (Product_{r>=1} (1 - x^r))*x^(k^2)/Product_{i=1..k} ((1 - x^i)^2) with k=3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 3, 1, -1, -3, -7, -10, -13, -16, -18, -18, -18, -15, -11, -5, 2, 11, 20, 30, 39, 48, 55, 60, 63, 63, 59, 53, 43, 29, 14, -5, -26, -47, -69, -92, -111, -130, -146, -157, -164, -168, -163, -155, -141, -120, -94, -65, -28, 10, 51, 95
Offset: 0

Views

Author

N. J. A. Sloane, Aug 31 2014

Keywords

References

  • Fulman, Jason. Random matrix theory over finite fields. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 51--85. MR1864086 (2002i:60012). See top of page 70.

Crossrefs

k=0 gives A010815. Cf. A246575-A246578.

Programs

  • Maple
    fGL:=proc(k) local a,i,r;
a:=x^(k^2)/mul((1-x^i)^2,i=1..k);
a:=a*mul(1-x^r,r=1..101);
series(a,x,101);
seriestolist(%);
end;fGL(3);
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.