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!)
A292193 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 - j^k*x^j). 5
1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 6, 5, 1, 1, 9, 14, 14, 7, 1, 1, 17, 36, 46, 25, 11, 1, 1, 33, 98, 164, 107, 56, 15, 1, 1, 65, 276, 610, 505, 352, 97, 22, 1, 1, 129, 794, 2324, 2531, 2474, 789, 198, 30, 1, 1, 257, 2316, 8986, 13225, 18580, 7273, 2314, 354 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*j/d)) * A(n-j,k) for n > 0. - Seiichi Manyama, Nov 02 2017

EXAMPLE

Square array begins:

   1,  1,  1,   1,   1, ...

   1,  1,  1,   1,   1, ...

   2,  3,  5,   9,  17, ...

   3,  6, 14,  36,  98, ...

   5, 14, 46, 164, 610, ...

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0 or i=1, 1,

      `if`(i>n, 0, i^k*b(n-i, i, k))+b(n, i-1, k))

    end:

A:= (n, k)-> b(n$2, k):

seq(seq(A(n, d-n), n=0..d), d=0..12);  # Alois P. Heinz, Sep 11 2017

CROSSREFS

Columns k=0..2 give A000041, A006906, A077335.

Rows 0+1, 2 give A000012, A000051.

Main diagonal gives A292194.

Cf. A292166.

Sequence in context: A050446 A214868 A144048 * A258708 A113983 A199333

Adjacent sequences:  A292190 A292191 A292192 * A292194 A292195 A292196

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Sep 11 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 19 03:54 EST 2020. Contains 332032 sequences. (Running on oeis4.)