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
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Sep 05 2015
STATUS
approved