The number of partitions of [n] with exactly 3 blocks without peaks.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =9a(5) =27a(6) =75a(7) =197a(8) =503a(9) =1263a(10) =3132a(11) =7695a(12) =18784a(13) =45649a(14) =110585a(15) =267276a(16) =644907a(17) =1554208a(18) =3742321a(19) =9005265a(20) =21659603a(21) =52078400a(22) =125186565a(23) =300870586a(24) =723010749a(25) =1737273406a(26) =4174084259a(27) =10028409724a(28) =24092769583a(29) =57880137331