A160611 Numerator of Laguerre(n, -4).
1, 5, 17, 143, 355, 4043, 5177, 367271, 713723, 2410003, 109669391, 85569361, 11122330591, 245535162239, 52108328723, 70514170732823, 1753034045867, 3087820148584967, 3365163124738543, 15216530369586809, 9955926989110451149, 63735241273696485041
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..491
Programs
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Magma
[Numerator((&+[Binomial(n,k)*(4^k/Factorial(k)): k in [0..n]])): n in [0..30]]; // G. C. Greubel, May 12 2018
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Mathematica
Numerator[Table[LaguerreL[n, -4], {n, 0, 50}]] (* G. C. Greubel, May 12 2018 *) -
PARI
for(n=0,30, print1(numerator(sum(k=0,n, binomial(n,k)*(4^k/k!))), ", ")) \\ G. C. Greubel, May 12 2018
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PARI
a(n) = numerator(pollaguerre(n, 0, -4)); \\ Michel Marcus, Feb 05 2021
Formula
a:= n-> numer(add(binomial(n, i)*4^i/i!, i=0..n)):
seq(a(n), n=0..25); # Alois P. Heinz, Jun 27 2017