A109125 Column 7 of array illustrated in A089574 and related to A034261.
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
Examples
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).
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]
Programs
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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 *)
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)
Extensions
Extended beyond a(6) by R. J. Mathar, Jun 26 2010