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A265018
Total sum T(n,k) of number of lambda-parking functions of partitions lambda of n into distinct parts with largest part k; triangle T(n,k), n>=0, floor(sqrt(2n)+1/2)<=k<=n, read by rows.
4
1, 1, 2, 3, 3, 5, 4, 8, 7, 5, 16, 12, 9, 6, 40, 16, 11, 7, 34, 55, 20, 13, 8, 50, 73, 70, 24, 15, 9, 125, 132, 96, 85, 28, 17, 10, 281, 212, 119, 100, 32, 19, 11, 351, 469, 267, 142, 115, 36, 21, 12, 307, 642, 644, 322, 165, 130, 40, 23, 13
OFFSET
0,3
LINKS
R. Stanley, Parking Functions, 2011
FORMULA
T(A000217(n),n) = A000272(n+1).
EXAMPLE
Triangle T(n,k) begins:
00 : 1;
01 : 1;
02 : 2;
03 : 3, 3;
04 : 5, 4;
05 : 8, 7, 5;
06 : 16, 12, 9, 6;
07 : 40, 16, 11, 7;
08 : 34, 55, 20, 13, 8;
09 : 50, 73, 70, 24, 15, 9;
10 : 125, 132, 96, 85, 28, 17, 10;
11 : 281, 212, 119, 100, 32, 19, 11;
12 : 351, 469, 267, 142, 115, 36, 21, 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=ldegree(f)..degree(f)))(g(n$2, [])):
seq(T(n), n=0..20);
CROSSREFS
Row sums give A265016.
Column sums give A265130.
Cf. A000217, A000272, A002024, A265019 (the same read by columns).
Sequence in context: A029579 A106647 A130157 * A238792 A158745 A175108
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Nov 30 2015
STATUS
approved