login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235774 Let b(k) = A164555(k)/A027642(k), the sequence of "original" Bernoulli numbers with -1 instead of A164555(0)=1; then a(n) = numerator of the n-th term of the binomial transform of the b(k) sequence. 3
-1, -1, 1, 1, 59, 3, 169, 5, 179, 7, 533, 9, 26609, 11, 79, 13, 3523, 15, 56635, 17, -168671, 19, 857273, 21, -236304031, 23, 8553247, 25, -23749438409, 27, 8615841677021, 29, -7709321025917, 31, 2577687858559, 33, -26315271552988224913 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

(a(n)/A027642(n)) = -1, -1/2, 1/6, 1, 59/30, 3, 169/42, 5, 179/30, 7, 533/66, 9,.. .

Difference table for a(n)/A027642(n):

-1, -1/2,   1/6,      1,  59/30,     3, 169/42, ...

1/2, 2/3,   5/6,  29/30,  31/30, 43/42,  41/42, ... = A165161(n)/A051717(n+1)

1/6, 1/6,  2/15,   1/15, -1/105, -1/21, -1/105, ... not in the OEIS

0, -1/30, -1/15, -8/105, -4/105, 4/105,  8/105, ... etc.

Compare with the array in A190339.

LINKS

Table of n, a(n) for n=0..36.

FORMULA

(a(n+1) - a(n))/A027642(n) = A165161(n)/A051717(n+1).

(A164558(n) - a(n))/A027642(n) = 2's = A007395.

(a(n) - A164555(n))/A027642(n) = n - 2 = A023444(n).

MATHEMATICA

b[0] = -1; b[1] = 1/2; b[n_] := BernoulliB[n]; a[n_] := Sum[Binomial[n, k]*b[k], {k, 0, n}] // Numerator; Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Jan 30 2014 *)

CROSSREFS

Cf. A164558/A027642, A165161(n)/A051717(n+1).

Sequence in context: A230852 A104380 A051321 * A088665 A198378 A159250

Adjacent sequences:  A235771 A235772 A235773 * A235775 A235776 A235777

KEYWORD

sign,frac

AUTHOR

Paul Curtz, Jan 15 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)