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A089273
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Fifth column (k=6) of array A078739(n,k) ((2,2)-generalized Stirling2).
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2
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1, 188, 12052, 540080, 20447056, 706827968, 23178048832, 736079932160, 22912552596736, 704164858293248, 21462936995648512, 650674662791229440, 19656291799888777216, 592413643343696150528, 17826953303927872110592
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The numerator of the g.f. is the m=3 row polynomial of the triangle A089275.
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REFERENCES
| P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003), 198-205.
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LINKS
| P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.
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FORMULA
| G.f. (1+118*x+ 600*x^2)/product(1-(p+1)*p*x, p=1..5).
a(n)= 2^n - 36*6^n + 36*6*12^n - 400*20^n + 75*3*30^n)/6 = d(n) + 118*d(n-1) + 600*d(n-2), n>=2, with d(n) := A089274(n)= A071951(n+5, 5)= (16875*30^n - 20000*20^n + 6048*12^n - 405*6^n + 2*2^n)/2520.
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MAPLE
| a := n-> (Matrix([[12052, 188, 1, 0, 0]]). Matrix(5, (i, j)-> if (i=j-1) then 1 elif j=1 then [70, -1708, 17544, -72000, 86400][i] else 0 fi)^n)[1, 3]; seq (a(n), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 14 2008]
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CROSSREFS
| Cf. A089272, A071951(Legendre-Stirling triangle).
Sequence in context: A064115 A185241 A204071 * A035832 A065612 A088264
Adjacent sequences: A089270 A089271 A089272 * A089274 A089275 A089276
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Nov 07 2003
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