This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A292830 #21 Jan 08 2025 13:01:46 %S A292830 1,3,85,5558,651186,119617025,31697064295,11444459810700, %T A292830 5400661033684164,3227014932144214335,2381276769035483594793, %U A292830 2126703075527239956801538,2260781626706432961741917750,2820945601365221814523529200893,4082702018096881373945823658830923 %N A292830 a(1) = 1, for n>=2, a(n) = B(2*n-1, n), where B(n, x) is the Bernoulli polynomial. %C A292830 Note that B(2*n-1,n) is an 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 A292830 M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23. %F A292830 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 A292830 a := n -> `if`(n=1, 1, bernoulli(2*n-1, n)): # _Peter Luschny_, Sep 25 2017 %t A292830 Array[Ceiling@ BernoulliB[2 # - 1, #] &, 15] (* _Michael De Vlieger_, Sep 24 2017 *) %o A292830 (PARI) a(n) = if (n==1, 1, subst(bernpol(2*n-1), x, n)); \\ _Michel Marcus_, Sep 25 2017 %Y A292830 Cf. A291897. %K A292830 nonn %O A292830 1,2 %A A292830 _Vladimir Shevelev_, Sep 24 2017 %E A292830 More terms from _Peter J. C. Moses_, Sep 24 2017