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 1-5 of 5 results.

A127238 Diagonal sums of Thue-Morse binomial triangle A127236.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 3, 6, 4, 4, 5, 4, 3, 4, 3, 6, 8, 6, 6, 6, 9, 10, 8, 8, 12, 7, 7, 7, 7, 7, 6, 8, 13, 12, 8, 7, 12, 8, 13, 14, 12, 15, 13, 12, 12, 13, 14, 13, 12, 15, 12, 12, 12, 15, 14, 17, 17, 22, 17, 22, 14, 15
Offset: 0

Views

Author

Paul Barry, Jan 10 2007

Keywords

Formula

a(n)=sum{k=0..floor(n/2), A010060(binomial(n-k,k))}

A127239 Central coefficients of Thue-Morse binomial triangle A127236.

Original entry on oeis.org

1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0
Offset: 0

Views

Author

Paul Barry, Jan 10 2007

Keywords

Links

Crossrefs

Cf. A010060, A127236.

Programs

  • Maple
    tm:= proc(n) option remember;
  if n::even then procname(n/2^padic:-ordp(n, 2))
  else 1 - procname((n-1)/2)
  fi
end proc:
tm(0):= 0:
seq(tm(binomial(2*n,n)),n=0..100); # Robert Israel, May 07 2019
  • Mathematica
    Table[ThueMorse[Binomial[2n, n]], {n, 0, 100}] (* Jean-François Alcover, Jun 22 2020 *)

Formula

a(n) = A010060(binomial(2n,n)).

A127237 Row sums of Thue-Morse binomial triangle A127236.

Original entry on oeis.org

1, 2, 3, 2, 4, 2, 2, 8, 9, 4, 2, 6, 4, 8, 14, 6, 10, 12, 5, 10, 7, 16, 13, 12, 17, 14, 13, 12, 8, 16, 14, 14, 18, 16, 18, 14, 14, 20, 22, 14, 24, 20, 28, 18, 22, 16, 25, 30, 24, 24, 32, 26, 30, 32, 24, 30
Offset: 0

Views

Author

Paul Barry, Jan 10 2007

Keywords

Formula

a(n)=sum{k=0..n, A010060(binomial(n,k))}

A127240 Partial sums of central coefficients of Thue-Morse binomial triangle A127236.

Original entry on oeis.org

1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, 17, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23
Offset: 0

Views

Author

Paul Barry, Jan 10 2007

Keywords

Formula

a(n) = Sum_{k=0..n} A010060(binomial(2*k,k)).

A127233 a(n) = n!*(n*(n+1)/2)!.

Original entry on oeis.org

1, 1, 12, 4320, 87091200, 156920924160000, 36785478363630796800000, 1536637256843037856927580160000000, 14998770936168817088309737749441675264000000000, 43408511507665453002645192043544271642563569306828800000000000
Offset: 0

Views

Author

Artur Jasinski, Jan 09 2007

Keywords

Crossrefs

Cf. A127234, A127236.

Programs

  • Maple
    seq(n!*(n*(n+1)/2)!,n=0..9); # Emeric Deutsch, Jan 20 2007
  • Mathematica
    Table[n!((n(n+1))/2)!,{n,0,10}] (* Harvey P. Dale, Aug 27 2021 *)

Extensions

More terms from Emeric Deutsch, Jan 20 2007
Showing 1-5 of 5 results.

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

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