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A065945
Bessel polynomial {y_n}''(2).
1
0, 0, 6, 210, 6390, 201810, 6895140, 257335596, 10489055220, 465303486780, 22363517407770, 1159112646836430, 64499453473280826, 3837361123234687230, 243168894263042103720, 16356164256377393353080, 1164094991704907423494920
OFFSET
0,3
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
FORMULA
From G. C. Greubel, Aug 14 2017: (Start)
a(n) = 4*n*(n - 1)*(1/2)_{n}*4^(n - 2)*hypergeometric1f1[(2-n, -2*n, 1).
E.g.f.: (-1/16)*(1 - 4*x)^(-5/2)*((56*x^2 - 44*x + 6)*sqrt(1 - 4*x) + (16*x^3 - 180*x^2 + 56*x - 6))*exp((1 - sqrt(1 - 4*x))/2). (End)
G.f.: (6*x^2/(1-x)^5)*hypergeometric2f0(3,5/2; - ; 4*x/(1-x)^2). - G. C. Greubel, Aug 16 2017
MATHEMATICA
Join[{0, 0}, Table[4*n*(n - 1)*Pochhammer[1/2, n]*4^(n - 2)* Hypergeometric1F1[2 - n, -2*n, 1], {n, 2, 50}]] (* G. C. Greubel, Aug 14 2017 *)
PROG
(PARI) for(n=0, 50, print1(sum(k=0, n-2, ((n+k+2)!/(4*k!*(n-k-2)!))), ", ")) \\ G. C. Greubel, Aug 14 2017
CROSSREFS
Sequence in context: A327248 A084694 A285149 * A076715 A029549 A183252
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 08 2001
STATUS
approved