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A121775 Triangle, read by rows, defined by: T(n,k) = Sum_{d|n} phi(n/d)*C(d,k) for n>0, k>=0, with T(0,0) = 1. 2
1, 1, 1, 2, 3, 1, 3, 5, 3, 1, 4, 8, 7, 4, 1, 5, 9, 10, 10, 5, 1, 6, 15, 20, 21, 15, 6, 1, 7, 13, 21, 35, 35, 21, 7, 1, 8, 20, 36, 60, 71, 56, 28, 8, 1, 9, 21, 42, 86, 126, 126, 84, 36, 9, 1, 10, 27, 59, 130, 215, 253, 210, 120, 45, 10, 1, 11, 21, 55, 165, 330, 462, 462, 330, 165, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

For n>0, (1/n)*Sum_{k=0..n} T(n,k)*(c-1)^k = number of n-bead necklaces with c colors: A000031 (c=2), A001867 (c=3), A001868 (c=4), A001869 (c=5), A054625 (c=6), A054626 (c=7), A054627 (c=8), A054628 (c=9), A054629 (c=10).

LINKS

Table of n, a(n) for n=0..75.

EXAMPLE

Triangle begins:

1;

1, 1;

2, 3, 1;

3, 5, 3, 1;

4, 8, 7, 4, 1;

5, 9, 10, 10, 5, 1;

6, 15, 20, 21, 15, 6, 1;

7, 13, 21, 35, 35, 21, 7, 1;

8, 20, 36, 60, 71, 56, 28, 8, 1;

9, 21, 42, 86, 126, 126, 84, 36, 9, 1;

10, 27, 59, 130, 215, 253, 210, 120, 45, 10, 1;

PROG

(PARI) T(n, k)=if(n<k|k<0, 0, if(n==0, 1, sumdiv(n, d, eulerphi(n/d)*binomial(d, k))))

CROSSREFS

Cf. A053635 (row sums), A121776 (antidiagonal sums), A054630.

Sequence in context: A035517 A099471 A243574 * A127951 A208814 A230449

Adjacent sequences:  A121772 A121773 A121774 * A121776 A121777 A121778

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Aug 23 2006

STATUS

approved

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Last modified October 17 21:24 EDT 2018. Contains 316293 sequences. (Running on oeis4.)