A292830 a(1) = 1, for n>=2, a(n) = B(2*n-1, n), where B(n, x) is the Bernoulli polynomial.

1, 3, 85, 5558, 651186, 119617025, 31697064295, 11444459810700, 5400661033684164, 3227014932144214335, 2381276769035483594793, 2126703075527239956801538, 2260781626706432961741917750, 2820945601365221814523529200893, 4082702018096881373945823658830923

Offset: 1

Author

Vladimir Shevelev, Sep 24 2017

Keywords

• nonn

Comments

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).

References

• M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.

Crossrefs

Cf. A291897.

Programs

Maple

a := n -> `if`(n=1, 1, bernoulli(2*n-1, n)): # Peter Luschny, Sep 25 2017

Mathematica

Array[Ceiling@ BernoulliB[2 # - 1, #] &, 15] (* Michael De Vlieger, Sep 24 2017 *)

PARI

a(n) = if (n==1, 1, subst(bernpol(2*n-1), x, n)); \\ Michel Marcus, Sep 25 2017

Formula

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)).

Extensions

More terms from Peter J. C. Moses, Sep 24 2017