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A109125
Column 7 of array illustrated in A089574 and related to A034261.
10
2, 41, 292, 1283, 4253, 11712, 28261, 61738, 124763, 236762, 426557, 735616, 1222064, 1965563, 3073176, 4686337, 6989056, 10217495, 14671058, 20725145, 28845727, 39605906, 53704631, 71987748, 95471569, 125369152, 163119491
OFFSET
0,1
LINKS
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