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 A320733 Number of partitions of n with two sorts of part 1 which are introduced in ascending order. 3
 1, 1, 3, 6, 13, 26, 54, 108, 219, 439, 882, 1766, 3539, 7081, 14172, 28351, 56716, 113443, 226908, 453833, 907698, 1815424, 3630893, 7261829, 14523725, 29047513, 58095121, 116190338, 232380810, 464761759, 929523710, 1859047619, 3718095507, 7436191301 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..3322 FORMULA G.f.: ((1 - x)/(1 - 2*x)) * Product_{k>=2} 1/(1 - x^k). - Ilya Gutkovskiy, Dec 03 2019 MAPLE b:= proc(n, i) option remember; `if`(n=0 or i<2, add(       Stirling2(n, j), j=0..2), add(b(n-i*j, i-1), j=0..n/i))     end: a:= n-> b(n\$2): seq(a(n), n=0..40); MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 2}], Sum[b[n - i j, i - 1], {j, 0, n/i}]]; a[n_] := b[n, n]; a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *) CROSSREFS Column k=2 of A292745. Cf. A002865, A011782, A090764. Sequence in context: A081254 A125049 A267581 * A164991 A213255 A215985 Adjacent sequences:  A320730 A320731 A320732 * A320734 A320735 A320736 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 20 2018 STATUS approved

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Last modified September 16 14:29 EDT 2021. Contains 347472 sequences. (Running on oeis4.)