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A275679 Number of set partitions of [n] with alternating block size parities. 3
1, 1, 1, 4, 3, 20, 43, 136, 711, 1606, 12653, 36852, 250673, 1212498, 6016715, 45081688, 196537387, 1789229594, 8963510621, 76863454428, 512264745473, 3744799424978, 32870550965259, 219159966518160, 2257073412153459, 15778075163815474, 165231652982941085 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..592

EXAMPLE

a(3) = 4: 123, 12|3, 13|2, 1|23.

a(4) = 3: 1234, 1|23|4, 1|24|3.

a(5) = 20: 12345, 1234|5, 1235|4, 123|45, 1245|3, 124|35, 125|34, 12|345, 12|3|45, 1345|2, 134|25, 135|24, 13|245, 13|2|45, 145|23, 14|235, 15|234, 1|2345, 14|2|35, 15|2|34.

MAPLE

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

      `if`((i+t)::odd, b(n-i, 1-t)*binomial(n-1, i-1), 0), i=1..n))

    end:

a:= n-> `if`(n=0, 1, b(n, 0)+b(n, 1)):

seq(a(n), n=0..35);

MATHEMATICA

b[n_, t_] := b[n, t] = If[n==0, 1, Sum[If[OddQ[i+t], b[n-i, 1-t] * Binomial[n-1, i-1], 0], {i, 1, n}]]; a[n_] := If[n==0, 1, b[n, 0] + b[n, 1]]; Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Feb 27 2017, translated from Maple *)

CROSSREFS

Cf. A003724, A005046, A007837, A038041, A275309, A275310, A275311, A275312, A275313, A286076.

Sequence in context: A280615 A281042 A076589 * A326818 A259229 A052039

Adjacent sequences:  A275676 A275677 A275678 * A275680 A275681 A275682

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 05 2016

STATUS

approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)