A384733 a(n) = 5*binomial(n,6) + 2*binomial(n,4).
0, 0, 0, 0, 2, 10, 35, 105, 280, 672, 1470, 2970, 5610, 10010, 17017, 27755, 43680, 66640, 98940, 143412, 203490, 283290, 387695, 522445, 694232, 910800, 1181050, 1515150, 1924650, 2422602, 3023685, 3744335, 4602880, 5619680, 6817272, 8220520, 9856770, 11756010
Offset: 0
Keywords
Examples
6*a(4) = 6*2 = 12 since the words are the 12 permutations of abcc. 6*a(7) = 6*105 = 630 since the words are the 420 permutations of abcceee and the 210 permutations of abdddde.
Links
- Paolo Xausa, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Crossrefs
Cf. A384686.
Programs
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Mathematica
A384733[n_] := 5*Binomial[n, 6] + 2*Binomial[n, 4]; Array[A384733, 50, 0] (* Paolo Xausa, Jun 11 2025 *)
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Python
def A384733(n): return n*(n*(n*(n*(n*(n-15)+97)-297)+406)-192)//144 # Chai Wah Wu, Jun 11 2025
Formula
a(n) = -(4/3)*n + (203/72)*n^2 - (33/16)*n^3 + (97/144)*n^4 - (5/48)*n^5 + (1/144)*n^6.
G.f.: (7*x^6 - 4*x^5 + 2*x^4)/(1-x)^7.
E.g.f.: exp(x)*(x^4/12 + x^6/144).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 6. - Chai Wah Wu, Jun 11 2025
Comments