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A168016 Triangle T(n,k) read by rows in which row n list the number of partitions of n into parts divisible by k for k=n,n-1,...,1. 7
1, 1, 2, 1, 0, 3, 1, 0, 2, 5, 1, 0, 0, 0, 7, 1, 0, 0, 2, 3, 11, 1, 0, 0, 0, 0, 0, 15, 1, 0, 0, 0, 2, 0, 5, 22, 1, 0, 0, 0, 0, 0, 3, 0, 30, 1, 0, 0, 0, 0, 2, 0, 0, 7, 42, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 1, 0, 0, 0, 0, 0, 2, 0, 3, 5, 11, 77, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 1, 0, 0, 0, 0, 0, 0, 2, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..100.

FORMULA

T(n,k) = A000041(n/k) if k|n; otherwise T(n,k) = 0. In particular, T(n,1) = A000041(n).

EXAMPLE

Triangle begins:

==============================================

.... k: 12 11 10. 9. 8. 7. 6. 5. 4. 3.. 2.. 1.

==============================================

n=1 ....................................... 1,

n=2 ................................... 1 , 2,

n=3 ............................... 1 , 0 , 3,

n=4 ............................ 1, 0 , 2 , 5,

n=5 ......................... 1, 0, 0 , 0 , 7,

n=6 ...................... 1, 0, 0, 2 , 3, 11,

n=7 ................... 1, 0, 0, 0, 0 , 0, 15,

n=8 ................ 1, 0, 0, 0, 2, 0 , 5, 22,

n=9 ............. 1, 0, 0, 0, 0, 0, 3 , 0, 30,

n=10 ......... 1, 0, 0, 0, 0, 2, 0, 0 , 7, 42,

n=11 ...... 1, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 56,

n=12 ... 1, 0, 0, 0, 0, 0, 2, 0, 3, 5 ,11, 77,

...

CROSSREFS

Cf. A000005, A000041, A035363, A035444, A135010, A138121, A168014, A168015, A168020, A168021.

Sequence in context: A247492 A113214 A280494 * A029323 A194849 A071802

Adjacent sequences:  A168013 A168014 A168015 * A168017 A168018 A168019

KEYWORD

easy,nonn,tabl

AUTHOR

Omar E. Pol, Nov 21 2009

EXTENSIONS

Edited and extended by Max Alekseyev, May 07 2010

STATUS

approved

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Last modified October 22 06:54 EDT 2019. Contains 328315 sequences. (Running on oeis4.)