|
| |
|
|
A003724
|
|
Number of partitions of n-set into odd blocks.
(Formerly M1427)
|
|
20
| |
|
|
1, 1, 1, 2, 5, 12, 37, 128, 457, 1872, 8169, 37600, 188685, 990784, 5497741, 32333824, 197920145, 1272660224, 8541537105, 59527313920, 432381471509, 3252626013184, 25340238127989, 204354574172160, 1699894200469849
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
REFERENCES
| L. Comtet, Analyse Combinatoire, Presses Univ. de France, 1970, Vol. II, pages 61-62.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 225, 2nd line of table.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565
|
|
|
FORMULA
| E.g.f.: exp ( sinh x ).
a(n)=sum(1/2^k*sum((-1)^i*binomial(k,i)*(k-2*i)^n,i,0,k)/k!,k,1,n); [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 22 2010]
a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator sqrt(1+x^2)*d/dx. Cf. A002017 and A009623. - Peter Bala, Dec 06 2011
|
|
|
MATHEMATICA
| a[n_] := Sum[((-1)^i*(k - 2*i)^n*Binomial[k, i])/(2^k*k!), {k, 1, n}, {i, 0, k}]; a[0] = 1; Table[a[n], {n, 0, 24}] (* From Jean-François Alcover, Dec 21 2011, after Vladimir Kruchinin *)
|
|
|
PROG
| (Maxima) a(n):=sum(1/2^k*sum((-1)^i*binomial(k, i)*(k-2*i)^n, i, 0, k)/k!, k, 1, n); /* From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 22 2010 */
|
|
|
CROSSREFS
| See A136630 for the table of partitions of an n-set into k odd blocks.
For partitions into even blocks see A005046 and A156289.
Cf. A000009, A000110. A002017, A009623.
Sequence in context: A009598 A002216 A024717 * A138314 A115277 A130221
Adjacent sequences: A003721 A003722 A003723 * A003725 A003726 A003727
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
|
| |
|
|
