login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A285425 Square array A(n,k), n>=1, k>=0, read by antidiagonals, where column k is the expansion of Sum_{j>=1} (2*j - 1)^k*x^(2*j-1)/(1 - x^(2*j-1)). 2
1, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 10, 1, 2, 1, 1, 28, 1, 6, 2, 1, 1, 82, 1, 26, 4, 2, 1, 1, 244, 1, 126, 10, 8, 1, 1, 1, 730, 1, 626, 28, 50, 1, 3, 1, 1, 2188, 1, 3126, 82, 344, 1, 13, 2, 1, 1, 6562, 1, 15626, 244, 2402, 1, 91, 6, 2, 1, 1, 19684, 1, 78126, 730, 16808, 1, 757, 26, 12, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

A(n,k) is the sum of k-th powers of odd divisors of n.

LINKS

Table of n, a(n) for n=0..77.

Eric Weisstein's World of Mathematics, Odd Divisor Function

Index entries for sequences related to sums of divisors

FORMULA

G.f. of column k: Sum_{j>=1} (2*j - 1)^k*x^(2*j-1)/(1 - x^(2*j-1)).

EXAMPLE

Square array begins:

1,  1,   1,    1,    1,     1,  ...

1,  1,   1,    1,    1,     1,  ...

2,  4,  10,   28,   82,   244,  ...

1,  1,   1,    1,    1,     1,  ...

2,  6,  26,  126,  626,  3126,  ...

2,  4,  10,   28,   82,   244,  ...

MATHEMATICA

Table[Function[k, SeriesCoefficient[Sum[(2 i - 1)^k x^(2 i - 1)/(1 - x^(2 i - 1)), {i, 1, n}], {x, 0, n}]][j - n], {j, 0, 12}, {n, 1, j}] // Flatten

CROSSREFS

Columns k=0-5 give: A001227, A000593, A050999, A051000, A051001, A051002.

Cf. A109974, A279394, A292919.

Sequence in context: A294580 A294587 A064645 * A008307 A249694 A192005

Adjacent sequences:  A285422 A285423 A285424 * A285426 A285427 A285428

KEYWORD

nonn,tabl

AUTHOR

Ilya Gutkovskiy, May 14 2017

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 22 12:00 EST 2018. Contains 299452 sequences. (Running on oeis4.)