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.

A061159 Numerators in expansion of Euler transform of b(n) = 1/2.

Original entry on oeis.org

1, 1, 7, 17, 203, 455, 2723, 6001, 133107, 312011, 1613529, 3705303, 39159519, 88466147, 443939867, 1041952049, 40842931395, 93889422323, 460998957853, 1054706036923, 10194929714949, 23513104814105, 111438617932133, 255719229005751, 4864448363248503
Offset: 0

Views

Author

Vladeta Jovovic, Apr 17 2001

Keywords

Comments

Denominators of c(n) are 2^d(n), where d(n)=power of 2 in (2n)!, cf. A005187.

Crossrefs

Programs

  • Maple
    b:= proc(n) option remember; `if`(n=0, 1, add(add(
          d/2, d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
        end:
    a:= n-> numer(b(n)):
    seq(a(n), n=0..35);  # Alois P. Heinz, Jul 28 2017
  • Mathematica
    c[n_] := c[n] = If[n == 0, 1,
         (1/(2n)) Sum[c[n-k] DivisorSigma[1, k], {k, 1, n}]];
    a[n_] := Numerator[c[n]];
    Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Apr 24 2022 *)

Formula

Numerators of c(n), where c(n)=1/(2*n)*Sum_{k=1..n} c(n-k)*sigma(k), n>0, c(0)=1.

A061160 Numerators in expansion of Euler transform of b(n) = 1/3.

Original entry on oeis.org

1, 1, 5, 50, 215, 646, 8711, 25475, 105925, 3091270, 11691247, 36809705, 445872155, 1364113925, 5085042010, 50975292560, 183383680088, 588817265695, 19512559194875, 62369303509475, 224877933068647, 2214198452392027, 7686538660149565, 25124342108522750
Offset: 0

Views

Author

Vladeta Jovovic, Apr 17 2001

Keywords

Comments

Denominators of c(n) are 3^d(n), where d(n)=power of 3 in (3*n)!, cf. A004128.

Crossrefs

Programs

  • Maple
    b:= proc(n) option remember; `if`(n=0, 1, add(add(
          d/3, d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
        end:
    a:= n-> numer(b(n)):
    seq(a(n), n=0..30);  # Alois P. Heinz, Jul 28 2017
  • Mathematica
    c[n_] := c[n] = If[n == 0, 1,
         (1/(3n)) Sum[c[n-k] DivisorSigma[1, k], {k, 1, n}]];
    a[n_] := Numerator[c[n]];
    Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 24 2022 *)

Formula

Numerators of c(n), where c(n) = (1/(3*n))*Sum_{k=1..n} c(n-k)*sigma(k), n>0, c(0)=1.
Showing 1-2 of 2 results.