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!)
A134285 Triangle of numbers obtained from the partition array A134284. 5
1, 3, 1, 10, 3, 1, 35, 19, 3, 1, 126, 65, 19, 3, 1, 462, 331, 92, 19, 3, 1, 1716, 1190, 421, 92, 19, 3, 1, 6435, 5587, 1805, 502, 92, 19, 3, 1, 24310, 20613, 8771, 2075, 502, 92, 19, 3, 1, 92378, 92821, 35726, 10616, 2318, 502, 92, 19, 3, 1, 352716, 347930, 160205 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This triangle is called s2(3)'.

LINKS

Table of n, a(n) for n=1..58.

Wolfdieter Lang, First 10 rows and more.

FORMULA

a(n,m) = sum(product(s2(3;j,1)^e(n,m,q,j),j=1..n),k=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. s2(3;n,1) = A035324(n,1) = A001700(n-1) = binomial(2*n-1,n).

Row sums = A001700. Triangle A134285 = A001263 * A000012. - Gary W. Adamson, Nov 19 2007

EXAMPLE

Triangle starts:

1

3, 1

10, 3, 1

35, 19, 3, 1

126, 65, 19, 3, 1

...

a(4,2)=19 because the m=2 parts partitions (1^1,3^1) and (2^2) of n=4 lead to 1^1*10^1 + 3^2 =19, since A001700(n-1)=[1,3,10,...], n>=1.

CROSSREFS

Row sums A134826. Alternating row sums A134827.

Cf. A001700.

Sequence in context: A257254 A126953 A134284 * A141811 A291538 A280787

Adjacent sequences:  A134282 A134283 A134284 * A134286 A134287 A134288

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Nov 13 2007

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 March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)