|
| |
|
|
A036074
|
|
E.g.f.: exp((exp(p*x)-p-1)/p+exp(x)) for p=4.
|
|
8
| |
|
|
1, 2, 9, 55, 412, 3619, 36333, 408888, 5080907, 68914023, 1011165446, 15935379409, 268125052373, 4792458452162, 90605469012877, 1805135197261131, 37775862401203916, 827992670793489263
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.
T. S. Motzkin, Sorting numbers ...: for a link to this paper see A000262.
|
|
|
LINKS
| Index entries for sequences related to sorting
Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565
|
|
|
FORMULA
| a(n)=sum(sum(binomial(m,i)*sum(binomial(i,j)*(1/4)^j*(3*j+i)^n,j,0,i)*(-5/4)^(m-i),i,0,m)/m!,m,1,n), n>0. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 14 2010]
|
|
|
PROG
| (Other) a(n):=sum(sum(binomial(m, i)*sum(binomial(i, j)*(1/4)^j*(3*j+i)^n, j, 0, i)*(-5/4)^(m-i), i, 0, m)/m!, m, 1, n); (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 14 2010]
|
|
|
CROSSREFS
| Cf. A001861, A002872-A002875, A036076, ...
Sequence in context: A075679 A001757 A078455 * A009363 A069564 A109366
Adjacent sequences: A036071 A036072 A036073 * A036075 A036076 A036077
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 11 2008 at the suggestion of Franklin T. Adams-Watters.
|
| |
|
|
