OFFSET
0,1
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). [From R. J. Mathar, Jun 26 2010]
FORMULA
From R. J. Mathar, Jun 26 2010: (Start)
a(n) = A105552(11+n,5+n).
G.f.: x*(-2-23*x+5*x^2+37*x^3-26*x^4-9*x^5+17*x^6-7*x^7+x^8)/(x-1)^9. a(n) = -1+1277*n/840 -19*n^3/480 -67*n^2/480 +41*n^5/80 +257*n^6/2800 +23*n^7/3360 +6049*n^4/5760 +n^8/5760. (End)
EXAMPLE
a(1) = 2 because 4+4+4 and 3+3+3+3 cannot be permuted. a(2) = 41 because there are 3 + 7 + 12 + 9 + 10 ways of permuting the associated partitions.
5553 (3 ways), 4441 & 544 (4+3 ways), 4432 (12 ways), 33331 & 4333 (5 + 4 ways) and 33322 (in 10 ways).
MATHEMATICA
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {2, 41, 292, 1283, 4253, 11712, 28261, 61738, 124763}, 30] (* Harvey P. Dale, Aug 21 2024 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Alford Arnold, Jun 19 2005
EXTENSIONS
Extended beyond a(6) by R. J. Mathar, Jun 26 2010
STATUS
approved