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A127947
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Hankel transform of central coefficients of (1+k*x+5x^2)^n, k arbitrary integer.
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1
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OFFSET
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0,2
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COMMENTS
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Hankel transform of A098264. The Hankel transform of e.g.f. Bessel_I(0,2*sqrt(5)x) and its k-th binomial transforms, are given by a(n). In general, the Hankel transform of e.g.f. Bessel_I(0,2*sqrt(m)x) and its binomial transforms is 2^n*m^C(n+1,2).
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LINKS
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FORMULA
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a(n) = 2^n*5^C(n+1,2).
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MATHEMATICA
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Table[2^n*5^Binomial[n+1, 2], {n, 0, 30}] (* G. C. Greubel, May 03 2018 *)
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PROG
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(PARI) for(n=0, 30, print1(2^n*5^binomial(n+1, 2), ", ")) \\ G. C. Greubel, May 03 2018
(Magma) [2^n*5^Binomial(n+1, 2): n in [0..30]]; // G. C. Greubel, May 03 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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