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 A115278 Number of partitions of {1,...,2*n} into even sized blocks such that no block size is repeated. 4
 1, 1, 1, 16, 29, 256, 14422, 49141, 490429, 10758400, 1797335306, 9458619391, 133756636598, 2528529510391, 137864810180749, 53441183229799381, 410251032050409469, 7615997734377068128, 167055180095977694194, 6741819165851219788075, 738863335901972011745434 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..370 FORMULA E.g.f.: B(x) of b(n) where b(2*n)=a(n), b(2*n+1)=0. B(x)=Product {m >= 1} (1+x^(2*m)/(2*m)!). MAPLE with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(       multinomial(n, n-i*j, i\$j)/j!*b(n-i*j, i-2), j=0..min(1, n/i))))     end: a:= n-> b(2*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[multinomial[n, Join[{n - i*j}, Array[i &, j]]]/j!* b[n - i*j, i - 2], {j, 0, Min[1, n/i]}]]]; a[n_] := b[2 n, 2 n]; Table[ a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 22 2016, after Alois P. Heinz *) CROSSREFS Cf. A005046, A007837, A032310, A115277. Sequence in context: A246345 A054314 A222545 * A228664 A217715 A064634 Adjacent sequences:  A115275 A115276 A115277 * A115279 A115280 A115281 KEYWORD nonn AUTHOR Christian G. Bower, Jan 18 2006 STATUS approved

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Last modified May 27 17:53 EDT 2020. Contains 334664 sequences. (Running on oeis4.)