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 A032021 Number of compositions (ordered partitions) of n into distinct odd parts. 26
 1, 1, 0, 1, 2, 1, 2, 1, 4, 7, 4, 7, 6, 13, 6, 19, 32, 25, 32, 31, 58, 43, 82, 49, 132, 181, 156, 193, 230, 325, 278, 457, 376, 715, 448, 967, 1290, 1345, 1386, 1723, 2276, 2341, 3116, 2959, 4750, 3823, 6358, 4681, 9480, 10945, 11832, 12169, 16442, 18793, 21002, 25537, 27820, 37687 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 C. G. Bower, Transforms (2) FORMULA "AGK" (ordered, elements, unlabeled) transform of 1, 0, 1, 0...(odds) G.f.: sum(k>=0, k! * x^(k^2) / prod(j=1..k, 1-x^(2*j) ) ). - Vladeta Jovovic, Aug 05 2004 MAPLE b:= proc(n, i) b(n, i):= `if`(n=0, [1], `if`(i<1, [], zip((x, y)        ->x+y, b(n, i-2), [0, `if`(i>n, [], b(n-i, i-2))[]], 0)))     end: a:= proc(n) local l; l:= b(n, n-1+irem(n, 2));       a(n):= add(l[i]*(i-1)!, i=1..nops(l))     end: seq(a(n), n=0..100);  # Alois P. Heinz, Nov 09 2012 MATHEMATICA b[n_, i_] := If[n == 0, {1}, If[i<1, {}, Plus @@ PadRight[{b[n, i-2], Join[{0}, If[i>n, {}, b[n-i, i-2]]]}]]]; a[n_] := Module[{l}, l = b[n, n-1+Mod[n, 2]]; Sum[l[[i]]*(i-1)!, {i, 1, Length[l]}]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *) PROG (PARI) N=66;  q='q+O('q^N); gf=sum(k=0, N, k! * q^(k^2) / prod(j=1, k, 1-q^(2*j) ) ); Vec(gf) /* Joerg Arndt, Sep 17 2012 */ CROSSREFS Cf. A032020, A000700. Sequence in context: A331982 A106380 A076198 * A306703 A295686 A246996 Adjacent sequences:  A032018 A032019 A032020 * A032022 A032023 A032024 KEYWORD nonn AUTHOR EXTENSIONS Prepended a(0)=1, Joerg Arndt, Oct 20 2012 STATUS approved

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)