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 A265017 Total sum T(n,k) of number of lambda-parking functions of partitions lambda of n into distinct parts with smallest part k; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 2
 1, 0, 1, 0, 0, 2, 0, 3, 0, 3, 0, 5, 0, 0, 4, 0, 7, 8, 0, 0, 5, 0, 25, 12, 0, 0, 0, 6, 0, 36, 16, 15, 0, 0, 0, 7, 0, 81, 20, 21, 0, 0, 0, 0, 8, 0, 107, 74, 27, 24, 0, 0, 0, 0, 9, 0, 316, 102, 33, 32, 0, 0, 0, 0, 0, 10, 0, 427, 222, 39, 40, 35, 0, 0, 0, 0, 0, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Rows n = 0..100, flattened R. Stanley, Parking Functions, 2011 EXAMPLE Triangle T(n,k) begins: 00 :  1; 01 :  0,   1; 02 :  0,   0,   2; 03 :  0,   3,   0,   3; 04 :  0,   5,   0,   0,  4; 05 :  0,   7,   8,   0,  0,  5; 06 :  0,  25,  12,   0,  0,  0, 6; 07 :  0,  36,  16,  15,  0,  0, 0, 7; 08 :  0,  81,  20,  21,  0,  0, 0, 0, 8; 09 :  0, 107,  74,  27, 24,  0, 0, 0, 0, 9; 10 :  0, 316, 102,  33, 32,  0, 0, 0, 0, 0, 10; 11 :  0, 427, 222,  39, 40, 35, 0, 0, 0, 0,  0, 11; 12 :  0, 869, 286, 153, 48, 45, 0, 0, 0, 0,  0,  0, 12; 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`(i*(i+1)/2n, 0, g(n-i, i-1, [i, l[]])))): T:= n-> (f-> seq(coeff(f, x, i), i=0..n))(g(n\$2, [])): seq(T(n), n=0..16); CROSSREFS Row sums give A265016. Column k=0 gives A000007. Main diagonal gives A028310, first lower diagonal is A000004. T(2n+1,n) gives A005563. T(2n+2,n) gives A028347(n+2). T(2n+3,n) gives A028560. Sequence in context: A161123 A035442 A213177 * A035376 A259708 A029220 Adjacent sequences:  A265014 A265015 A265016 * A265018 A265019 A265020 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Nov 30 2015 STATUS approved

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Last modified October 18 16:18 EDT 2018. Contains 316323 sequences. (Running on oeis4.)