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A065920
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Bessel polynomial {y_n}'(2).
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7
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0, 1, 15, 246, 4810, 111315, 2994621, 92069740, 3188772756, 122934101445, 5223324100555, 242563221769506, 12224586738476190, 664572113979550231, 38767776344788218105, 2415639337342677314520, 160131212043826343202856
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OFFSET
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0,3
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REFERENCES
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J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
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LINKS
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FORMULA
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Recurrence: (n-1)^2*a(n) = (2*n - 1)*(2*n^2 - 2*n + 1)*a(n-1) + n^2*a(n-2). - Vaclav Kotesovec, Jul 22 2015
a(n) = 2*n*(1/2)_{n}*4^(n - 1)* hypergeometric1f1(1 - n, -2*n, 1).
E.g.f.: ((1 - 4*x)^(3/2) + 2*x*(1 - 4*x)^(1/2) + 8*x - 1)*exp((1 - sqrt(1 - 4*x))/2)/(4*(1 - 4*x)^(3/2)). (End)
G.f.: (t/(1-t)^3)*hypergeometric2f0(2,3/2; - ; 4*t/(1-t)^2). - G. C. Greubel, Aug 16 2017
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MATHEMATICA
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Table[Sum[(n+k+1)!/(2*(n-k-1)!*k!), {k, 0, n-1}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 22 2015 *)
Join[{0}, Table[2*n*Pochhammer[1/2, n]*4^(n - 1)* Hypergeometric1F1[1 - n, -2*n, 1], {n, 1, 50}]] (* G. C. Greubel, Aug 14 2017 *)
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PROG
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(PARI) for(n=0, 50, print1(sum(k=0, n-1, (n+k+1)!/(2*(n-k-1)!*k!)), ", ")) \\ G. C. Greubel, Aug 14 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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