A090643 - OEIS

A090643

a(n)=(-1)^(n+1)*(3/4)*(9^n-1)*B(2n) where B(k) denotes the k-th Bernoulli number.

0, 1, 2, 13, 164, 3355, 100886, 4185097, 228970568, 15972720439, 1383706615610, 145736540156581, 18339615566386412, 2717605030233712723, 468371974894477377374, 92895125380418204480065, 21008128723110866359626896, 5373571097376355083238621807

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = (2n)! [x^(2n)] (3/2) x sin(x)/(2 cos(x)+1). - Ira M. Gessel Feb 23 2012

a(n) = (-1)^n*(Sum_{i, 0, 2*n - 1} (Bernoulli(i)*binomial(2*n, i)*3^i))/2. - Detlef Meya, Apr 14 2024

a(n) ~ sqrt(Pi) * 3^(2*n+1) * n^(2*n + 1/2) / (Pi^(2*n) * exp(2*n)). - Vaclav Kotesovec, Apr 14 2024

MATHEMATICA

a[n_]:=(-1)^n*Sum[BernoulliB[i]*Binomial[2*n, i]*3^i, {i, 0, 2*n-1}]/2; Flatten[Table[a[n], {n, 0, 17}]] (* Detlef Meya, Apr 14 2024 *)

PROG

(PARI) a(n)=(-1)^(n+1)*(3/4)*(9^n-1)*bernfrac(2*n)

CROSSREFS

Sequence in context: A187927 A252766 A098638 * A132521 A380772 A360601

Adjacent sequences: A090640 A090641 A090642 * A090644 A090645 A090646

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Dec 13 2003

STATUS

approved