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A205810 Irregular triangle read by rows: Whitney numbers c_{n,k} (n >= 0, 0 <= k <= 2n) of Lucas lattices. 1
1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 3, 4, 3, 3, 1, 1, 4, 6, 8, 9, 8, 6, 4, 1, 1, 5, 10, 15, 20, 21, 20, 15, 10, 5, 1, 1, 6, 15, 26, 39, 48, 52, 48, 39, 26, 15, 6, 1, 1, 7, 21, 42, 70, 98, 119, 127, 119, 98, 70, 42, 21, 7, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..63.

E. Munarini, N. Zagaglia Salvi, On the Rank Polynomial of the Lattice of Order Ideals of Fences and Crowns, Discrete Mathematics 259 (2002), 163-177.

FORMULA

c(n,k) = n*Sum_{i=0..floor(k/2)} 1/(n-i)*binomial(n-i,n-k+i)*binomial(k-i-1,i) for 0<=k<=2*n-1; c(n,2*n) = 1. - Leonid Bedratyuk, May 15 2018

EXAMPLE

Triangle begins:

  1;

  1, 1,  1;

  1, 2,  1,  2,  1;

  1, 3,  3,  4,  3,  3,   1;

  1, 4,  6,  8,  9,  8,   6,   4,   1;

  1, 5, 10, 15, 20, 21,  20,  15,  10,  5,  1;

  1, 6, 15, 26, 39, 48,  52,  48,  39, 26, 15,  6,  1;

  1, 7, 21, 42, 70, 98, 119, 127, 119, 98, 70, 42, 21, 7, 1;

  ...

MAPLE

c:= (n, k)-> `if`(k=2*n, 1, n*add(1/(n-i)*binomial(n-i, n-k+i)*binomial(k-i-1, i), i=0..floor(k/2))): seq(seq(c(n, k), k=0..2*n), n=0..8);  # Leonid Bedratyuk, May 15 2018

PROG

(PARI) T(n, k) = if (k==2*n, 1, n*sum(i=0, k\2, 1/(n-i)*binomial(n-i, n-k+i)*binomial(k-i-1, i)));

tabf(nn) = for (n=0, nn, for (k=0, 2*n, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 16 2018

CROSSREFS

Main diagonal is A051292.

Sequence in context: A075119 A224076 A137278 * A139368 A266506 A134303

Adjacent sequences:  A205807 A205808 A205809 * A205811 A205812 A205813

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Jan 31 2012

STATUS

approved

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Last modified August 7 09:16 EDT 2020. Contains 336274 sequences. (Running on oeis4.)