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 A274538 Number of set partitions of [n] such that each element is contained in a block whose index parity coincides with the parity of the element. 3
 1, 1, 1, 2, 3, 7, 14, 39, 95, 304, 865, 3103, 10038, 39773, 143473, 620382, 2461099, 11504723, 49658054, 249102263, 1159930119, 6205900348, 30959905841, 175763987955, 934068692102, 5602484594053, 31563436487785, 199267671153562, 1185224170637619 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS All odd elements are in blocks with an odd index and all even elements are in blocks with an even index. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..662 Wikipedia, Partition of a set FORMULA a(n) = Sum_{k=0..n} A274537(n,k). EXAMPLE a(3) = 2: 13|2, 1|2|3. a(4) = 3: 13|24, 1|24|3, 1|2|3|4. a(5) = 7: 135|24, 13|24|5, 15|24|3, 1|24|35, 15|2|3|4, 1|2|35|4, 1|2|3|4|5. a(6) = 14: 135|246, 13|246|5, 13|24|5|6, 15|246|3, 15|24|3|6, 1|246|35, 1|24|35|6, 15|26|3|4, 15|2|3|46, 1|26|35|4, 1|2|35|46, 1|26|3|4|5, 1|2|3|46|5, 1|2|3|4|5|6. MAPLE b:= proc(n, m, t) option remember; `if`(n=0, 1, add(       `if`(irem(j, 2)=t, b(n-1, max(m, j), 1-t), 0), j=1..m+1))     end: a:= n-> b(n, 0, 1): seq(a(n), n=0..30); MATHEMATICA b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j, 2] == t, b[n - 1, Max[m, j], 1 - t], 0], {j, 1, m + 1}]]; a[n_] := b[n, 0, 1]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 23 2018, translated from Maple *) CROSSREFS Row sums of A274537. Column k=2 of A274835. Sequence in context: A296417 A296418 A006785 * A113182 A165433 A238728 Adjacent sequences:  A274535 A274536 A274537 * A274539 A274540 A274541 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 27 2016 STATUS approved

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Last modified November 28 07:52 EST 2021. Contains 349401 sequences. (Running on oeis4.)