The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102759 Number of partitions of n-set in which number of blocks of size 2k is even (or zero) for every k. 9
 1, 1, 1, 2, 8, 27, 82, 338, 1647, 7668, 37779, 210520, 1276662, 7985200, 51302500, 358798144, 2677814900, 20309850311, 160547934756, 1344197852830, 11666610870142, 104156661915427, 962681713955130, 9238216839975106, 91508384728188792, 930538977116673878 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 FORMULA E.g.f. for offset 2: exp(sinh(x))*Product_{k>=1} cosh(x^(2*k)/(2*k)!). - Geoffrey Critzer, Jan 02 2011 MAPLE with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,        add(`if`(irem(i, 2)=1 or irem(j, 2)=0, multinomial(        n, n-i*j, i\$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))     end: a:= n-> b(n\$2): seq(a(n), n=0..30);  # Alois P. Heinz, Mar 08 2015 MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[If[Mod[i, 2] == 1 || Mod[j, 2] == 0, multinomial[n, Join[{n-i*j}, Table[i, {j}]]]/j!*b[n-i*j, i-1], 0], {j, 0, n/i}]]] ; a[n_] := b[n, n]; Table[ a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 16 2015, after Alois P. Heinz *) PROG (PARI) N=31; x='x+O('x^N); Vec(serlaplace(exp(sinh(x))*prod(k=1, N, cosh(x^(2*k)/(2*k)!)))) /* gives: [1, 1, 1, 2, 8, 27, 82, 338, 1647, 7668, ...] , Joerg Arndt, Jan 03 2011 */ CROSSREFS Cf. A003483, A006950, A130219 - A130223. Sequence in context: A289864 A290056 A100505 * A292698 A261056 A295135 Adjacent sequences:  A102756 A102757 A102758 * A102760 A102761 A102762 KEYWORD nonn AUTHOR Vladeta Jovovic, Feb 10 2005, Aug 05 2007 EXTENSIONS Offset changed to 0 and two 1's prepended by Alois P. Heinz, Mar 08 2015 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.

Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)