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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)/2<n, 0, `if`(n=0, p(l)*x^

                `if`(l=[], 0, l[1]), g(n, i-1, l)+

                `if`(i>n, 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 June 25 03:03 EDT 2017. Contains 288708 sequences.