login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003724 Number of partitions of n-set into odd blocks.
(Formerly M1427)
22
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, 14594815769038848, 129076687233903673 (list; graph; refs; listen; history; text; 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 and Alois P. Heinz, Table of n, a(n) for n = 0..592 (first 101 terms from T. D. Noe)

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*C(k,i)*(k-2*i)^n, i=0..k)/k!, k=1..n). - Vladimir Kruchinin, 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

EXAMPLE

G.f. = 1 + x + x^2 + 2*x^3 + 5*x^4 + 12*x^5 + 37*x^6 + 128*x^7 + 457*x^8 + ...

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      binomial(n-1, j-1)*irem(j, 2)*a(n-j), j=1..n))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 17 2015

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}] (* Jean-Fran├žois Alcover, Dec 21 2011, after Vladimir Kruchinin *)

With[{nn=30}, CoefficientList[Series[Exp[Sinh[x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Apr 06 2012 *)

Table[Sum[BellY[n, k, Mod[Range[n], 2]], {k, 0, n}], {n, 0, 24}] (* Vladimir Reshetnikov, Nov 09 2016 *)

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); /* Vladimir Kruchinin, 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

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 26 00:51 EDT 2017. Contains 284111 sequences.