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 A265007 Total sum of number of lambda-parking functions, where lambda ranges over all partitions of n. 3
 1, 1, 3, 7, 18, 40, 97, 216, 499, 1112, 2502, 5503, 12197, 26582, 58088, 125619, 271713, 583228, 1251115, 2668651, 5685053, 12059993, 25544291, 53926003, 113666195, 238946232, 501546514, 1050430420, 2196869731, 4586021745, 9560876381, 19900839742, 41373446190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..50 R. Stanley, Parking Functions, 2011 EXAMPLE The number of lambda-parking functions induced by the partitions of 4: 1 by [1,1,1,1]: [1,1,1,1], 4 by [1,1,2]: [1,1,1], [1,1,2], [1,2,1], [2,1,1], 4 by [2,2]: [1,1], [1,2], [2,1], [2,2], 5 by [1,3]: [1,1], [1,2], [2,1], [1,3], [3,1], 4 by [4]: [1], [2], [3], [4]. a(4) = 1 + 4 + 4 + 5 + 4 = 18. MAPLE 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`(n=0 or i=1, p([1\$n, l[]]), g(n, i-1, l) +`if`(i>n, 0, g(n-i, i, [i, l[]]))): a:= n-> g(n\$2, []): seq(a(n), n=0..20); MATHEMATICA p[l_] := With[{n = Length[l]}, n! Det[Table[With[{t = j - i + 1}, If[t < 0, 0, l[[i]]^t/t!]], {i, n}, {j, n}]]]; g[n_, i_, l_] := If[n == 0 || i == 1, p[Join[ Table[1, {n}], l]], g[n, i - 1, l] + If[i > n, 0, g[n - i, i, Prepend[l, i]]]]; a[n_] := If[n == 0, 1, g[n, n, {}]]; Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Aug 22 2021, after Alois P. Heinz *) CROSSREFS Cf. A000041, A255047, A265016. Sequence in context: A208715 A302408 A076700 * A026533 A131630 A305652 Adjacent sequences: A265004 A265005 A265006 * A265008 A265009 A265010 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 29 2015 STATUS approved

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Last modified May 30 10:33 EDT 2023. Contains 363050 sequences. (Running on oeis4.)