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%I #18 Sep 26 2017 03:12:50
%S 1,3,85,5558,651186,119617025,31697064295,11444459810700,
%T 5400661033684164,3227014932144214335,2381276769035483594793,
%U 2126703075527239956801538,2260781626706432961741917750,2820945601365221814523529200893,4082702018096881373945823658830923
%N a(1) = 1, for n>=2, a(n) = B(2*n-1, n), where B(n, x) is the Bernoulli polynomial.
%C Note that B(2*n-1,n) is integer for all positive integer n, except for n=1, for which B(1,1) = 1/2, so for all n>=1, a(n) is the numerator of B(2*n-1,n). Also note that a(n) is always divisible by (2*n-1) (cf. formula).
%D M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.
%F From [Abramowitz and Stegun] for n >= 2 we have a(n) = (2*n - 1) * (1^(2*n - 2) + 2^(2*n - 2) + ... + (n-1)^(2*n - 2)).
%p a := n -> `if`(n=1, 1, bernoulli(2*n-1, n)): # _Peter Luschny_, Sep 25 2017
%t Array[Ceiling@ BernoulliB[2 # - 1, #] &, 15] (* _Michael De Vlieger_, Sep 24 2017 *)
%o (PARI) a(n) = if (n==1, 1, subst(bernpol(2*n-1), x, n)); \\ _Michel Marcus_, Sep 25 2017
%Y Cf. A291897.
%K nonn
%O 1,2
%A _Vladimir Shevelev_, Sep 24 2017
%E More terms from _Peter J. C. Moses_, Sep 24 2017
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