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A292830 a(1) = 1, for n>=2, a(n) = B(2*n-1, n), where B(n, x) is the Bernoulli polynomial. 0
1, 3, 85, 5558, 651186, 119617025, 31697064295, 11444459810700, 5400661033684164, 3227014932144214335, 2381276769035483594793, 2126703075527239956801538, 2260781626706432961741917750, 2820945601365221814523529200893, 4082702018096881373945823658830923 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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).

REFERENCES

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

LINKS

Table of n, a(n) for n=1..15.

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)).

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 *)

PROG

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

CROSSREFS

Cf. A291897.

Sequence in context: A042587 A156879 A120264 * A185142 A279020 A302947

Adjacent sequences:  A292827 A292828 A292829 * A292831 A292832 A292833

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Sep 24 2017

EXTENSIONS

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

STATUS

approved

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Last modified June 6 17:01 EDT 2020. Contains 334829 sequences. (Running on oeis4.)