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A096161 Row sums for triangle A096162. 8
1, 3, 8, 30, 133, 768, 5221, 41302, 369170, 3677058, 40338310, 483134179, 6271796072, 87709287104, 1314511438945, 21017751750506, 357102350816602, 6424883282375340, 122025874117476166, 2439726373093186274 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also, partitions such that a set of k equal terms are labeled 1 through k and can appear in any order. For example, the partition 3+2+2+2+1+1+1+1 of 13 appears 1!*3!*4!=144 times because there are 1! ways to order the one "3," 3! ways to order the three "2"s, ... - Christian G. Bower, Jan 17 2006

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..449

FORMULA

G.f.: B(x)*B(x^2)*B(x^3)*... where B(x) is g.f. of A000142. - Christian G. Bower, Jan 17 2006

G.f.: Product_{k>0} Sum_{r>=0} x^(r*k)*r!. - Andrew Howroyd, Dec 22 2017

EXAMPLE

1 1 2 1 3 6 1 4 6 12 24 ... A036038

1 1 1 1 3 1 1 4 3 6 1 ... A036040

1 1 2 1 1 6 1 1 2 2 24 ... A096162

so a(n) begins 1 3 8 30 ... A096161

PROG

(PARI) { my(n=25); Vec(prod(k=1, n, O(x*x^n) + sum(r=0, n\k, x^(r*k)*r!))) }

CROSSREFS

Cf. A005651, A000110, A036038, A036040, A096162.

Sequence in context: A213860 A162560 A293250 * A161779 A074501 A009123

Adjacent sequences:  A096158 A096159 A096160 * A096162 A096163 A096164

KEYWORD

nonn

AUTHOR

Alford Arnold, Jun 18 2004

EXTENSIONS

More terms from Vladeta Jovovic, Jun 22 2004

STATUS

approved

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Last modified October 19 09:20 EDT 2018. Contains 316339 sequences. (Running on oeis4.)