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 A032008 "AFK" (ordered, size, unlabeled) transform of 1,3,5,7,... 4
 1, 1, 3, 11, 17, 53, 161, 285, 569, 1459, 4699, 7177, 15631, 28229, 66883, 211311, 319929, 627705, 1163049, 2150209, 4422225, 14320583, 20392019, 39962165, 68618087, 126643545, 212615483, 433704811, 1312156393, 1864959757, 3502343041, 5919183485, 10364053441 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of compositions of n into distinct parts if there are (2i-1) kinds of part i. a(3) = 11: 3, 3', 3'', 3''', 3'''', 21, 2'1, 2''1, 12, 12', 12''. - Alois P. Heinz, Sep 05 2015 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..4000 C. G. Bower, Transforms (2) MAPLE b:= proc(n, i, p) option remember;       `if`(n=0, p!, `if`(i<1, 0, b(n, i-1, p)+       `if`(i>n, 0, (2*i-1)*b(n-i, i-1, p+1))))     end: a:= n-> b(n\$2, 0): seq(a(n), n=0..40);  # Alois P. Heinz, Sep 05 2015 MATHEMATICA b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 1, 0, b[n, i - 1, p] + If[i > n, 0, (2 i - 1)*b[n - i, i - 1, p + 1]]]]; a[n_] := b[n, n, 0]; a /@ Range[0, 40] (* Jean-François Alcover, Sep 11 2019, after Alois P. Heinz *) PROG (PARI) seq(n)={apply(p->subst(serlaplace(p), y, 1), Vec(prod(k=1, n, 1 + (2*k-1)*x^k*y + O(x*x^n))))} \\ Andrew Howroyd, Jun 21 2018 CROSSREFS Cf. A032005, A032006, A032007. Sequence in context: A078116 A245045 A127996 * A061368 A145701 A072982 Adjacent sequences:  A032005 A032006 A032007 * A032009 A032010 A032011 KEYWORD nonn AUTHOR EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Sep 05 2015 STATUS approved

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Last modified January 21 13:47 EST 2020. Contains 331113 sequences. (Running on oeis4.)