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A265016
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Total sum of number of lambda-parking functions, where lambda ranges over all partitions of n into distinct parts.
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7
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1, 1, 2, 6, 9, 20, 43, 74, 130, 241, 493, 774, 1413, 2286, 3987, 7287, 11650, 19235, 31581, 50852, 80867, 141615, 214538, 349179, 541603, 859759, 1303221, 2054700, 3277493, 4960397, 7652897, 11662457, 17703655, 26603187, 40043433, 59384901, 92234897, 134538472
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..100
Richard P. Stanley, Parking Functions, 2011.
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EXAMPLE
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The number of lambda-parking functions induced by the partitions of 4 into distinct parts:
5 by [1,3]: [1,1], [1,2], [2,1], [1,3], [3,1],
4 by [4]: [1], [2], [3], [4].
a(4) = 5 + 4 = 9.
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MAPLE
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p:= l-> (n-> n!*LinearAlgebra[Determinant](Matrix(n, (i, j)
-> (t->`if`(t<0, 0, l[i]^t/t!))(j-i+1))))(nops(l)):
g:= (n, i, l)-> `if`(i*(i+1)/2<n, 0, `if`(n=0, p(l),
g(n, i-1, l)+`if`(i>n, 0, g(n-i, i-1, [i, l[]])))):
a:= n-> g(n$2, []):
seq(a(n), n=0..35);
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MATHEMATICA
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p[l_] := With[{n = Length[l]}, n!*Det[Table[Function[t,
If[t < 0, 0, l[[i]]^t/t!]][j - i + 1], {i, n}, {j, n}]]];
g[n_, i_, l_] := If[i (i + 1)/2 < n, 0, If[n == 0, p[l],
g[n, i - 1, l] + If[i > n, 0, g[n - i, i - 1, Prepend[l, i]]]]];
a[n_] := If[n == 0, 1, g[n, n, {}]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Aug 20 2021, after Alois P. Heinz *)
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CROSSREFS
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Row sums of A265017, A265018, A265019, A265020.
Cf. A000009, A265007, A265202.
Sequence in context: A325040 A350949 A088902 * A279897 A336131 A095967
Adjacent sequences: A265013 A265014 A265015 * A265017 A265018 A265019
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Nov 30 2015
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STATUS
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approved
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