OFFSET
1,4
COMMENTS
a(n) = Sum(k*A121632(n,k), k>=0).
REFERENCES
E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..449
FORMULA
a(1)=0; a(n) = n*a(n-1)+(n-1)!-1 for n>=2.
a(n)= A000254(n)- A002672(n) a(n)= n!*sum(1/k,k=1..10)- floor(n!(e-1)) [From Gary Detlefs, Jul 18 2010]
D-finite with recurrence a(n) +(-2*n-1)*a(n-1) +(n^2+2*n-4)*a(n-2) +(-2*n^2+6*n-3)*a(n-3) +(n-3)^2*a(n-4)=0. - R. J. Mathar, Jul 26 2022
EXAMPLE
a(2)=0 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, all of whose columns start at level 0.
MAPLE
a[1]:=0: for n from 2 to 23 do a[n]:=n*a[n-1]+(n-1)!-1 od: seq(a[n], n=1..23);
MATHEMATICA
RecurrenceTable[{a[1]==0, a[n]==n*a[n-1]+(n-1)!-1}, a, {n, 20}] (* Harvey P. Dale, Dec 01 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 12 2006
STATUS
approved