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A173280
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First column of the matrix power A173279(.,.)^j in the limit j->infinity.
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3
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1, 1, 3, 7, 29, 129, 757, 5185, 41155, 368351, 3671635, 40295943, 482758111, 6268066531, 87668492115, 1314023850727, 21011431917453, 357014074280785, 6423561495057421, 122004755658629081, 2439367774898883497, 51213663674167659301, 1126452985959434543237
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OFFSET
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0,3
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COMMENTS
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We can generalize A173279 to other matrices derived from some sequence S by Smat(n,k) := S(n-r*k), r >= 2,
and find that they define sequences B(x) via S(x)= B(X)/B(x^r), b(n) = Sum_{t=0..n, n-t == 0 (mod r)} S(t)*B_{(n-t)/r}.
The sequence here is the case of S=A000142 and r=2.
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LINKS
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FORMULA
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A000142(x) = A(x)/A(x^2), where A(x) and A000142(x) are the o.g.f.'s associated with A000142 and this sequence here.
Sum_{n>=0} 1/a(n) = 2.519966353393413186683398448854995831308...
a(n) = Sum_{t=0..n, n-t even} t!*a_{(n-t)/2}. - R. J. Mathar, Feb 22 2010
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MAPLE
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A173280 := proc(n) option remember; local a, l; if n = 0 then 1; else a :=0 ; for l from n to 0 by -2 do a := a+ l!*procname((n-l)/2) : end do ; a ; end if; end proc:
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MATHEMATICA
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A173280[n_] := A173280[n] = Module[{a, l}, If[n == 0, 1, a = 0; For[l = n, l >= 0, l -= 2, a = a + l!*A173280[(n-l)/2]]; a]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Extended, and invalid comment on convergence to e removed, by R. J. Mathar, Feb 22 2010
Index of B in the convolution formula in the comment corrected by R. J. Mathar, Mar 23 2010
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STATUS
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approved
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