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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A228838 a(n) = n * A002445(n).

Original entry on oeis.org

0, 6, 60, 126, 120, 330, 16380, 42, 4080, 7182, 3300, 1518, 32760, 78, 12180, 214830, 8160, 102, 34545420, 114, 270600, 37926, 15180, 6486, 1113840, 1650, 41340, 21546, 24360, 10266, 1703601900, 186, 16320, 2135826, 1020, 164010, 5043631320, 222, 1140
Offset: 0

Views

Author

Paul Curtz, Sep 05 2013

Keywords

Comments

a(n+1) is a multiple of A040031(n+1), sequence of period 2: 6, 12.
a(n) is divisible by A040879(n)=30 followed by the sequence of period 2: 6, 60. See A040214 and A165734.
Note that A164877(n) + A000367(n) = A164558(2n).

Examples

			a(0)=0*1, a(1)=1*6, a(2)=2*30=60,, a(3)=3*42=126.

Links

Programs

  • PARI
    a(n)=n*denominator(bernfrac(2*n))

Formula

a(n) = A176328(2n) - A000367(n).
a(n) = A164877(n)/2.
a(n+1) = A111008(n) * A036283(n+1).
2*a(n) = A164558(2n) - A000367(n).
a(n) = A164558(2n) - A176328(2n).

Extensions

Typo in data fixed by Colin Barker, Jul 03 2015

A174263 Numerator of the n-th term of the inverse Binomial Transform of the Bernoulli sequence prefixed with 0.

Original entry on oeis.org

0, 1, -5, 14, -23, 349, -499, 793, -1038, 7901, -9791, 65488, -78193, 795259, -925389, 1615811, -1841036, 67142767, -75821437, 358067518, -388783203, -521129621, 480390923, 133108162049
Offset: 0

Views

Author

Paul Curtz, Mar 14 2010

Keywords

Comments

The inverse binomial transform of 0, 1, -1/2, 1/6, 0, ... is A(n) = 0, 1, -5/2, 14/3, -23/3, ... The current sequence is defined by the numerators; the denominators are A100650(n).
There is a connection to the sequence b(n) = 0, 1, 1/2, 1/6, 0, -1/30, ... of modified Bernoulli numbers [b(0)=0, b(2) = -Bernoulli(1), b(n) = Bernoulli(n-1) if n <> 2] discussed in A165142: The inverse binomial transform of b(n) is c(n) = 0, 1, -3/2, 5/3, -5/3, 49/30, -49/30, ..., and c(n) - A(n) = (-1)^n*A000217(n-1).

Crossrefs

Cf. A164558.

Programs

  • Maple
    read("transforms") ;
A174264 := proc(n) local b; b := [0,seq(bernoulli(i),i=0..n+1)] ; BINOMIALi(b) ; numer(op(n+1,%)) ; end proc:
seq(A174264(n),n=0..30) ; # R. J. Mathar, Jan 21 2011

A174356 (-1)^(n+1)*n*A174276(n).

Original entry on oeis.org

0, 2, -12, 90, -280, 1050, -13860, 70070, -48048, 4594590, -4618900, 106696590, -382444920, 966735770, -3123300180, 97045398450, -97241449760, 3409528332210, -3610088822340, 9399601637426, -13492251154200
Offset: 0

Views

Author

Paul Curtz, Mar 17 2010

Keywords

Comments

The sequence obeys a(n) = A174289(n) - A174290(n), a formula that might be compared to A164869(n) = n*A027642(n) = A164558(n)-A164555(n).
Previous Showing 11-13 of 13 results.

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

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