A058806 a(n) = n! * H_n(n) where H_0(n) = 1/n, H_m(n) = Sum_{k=1..n} H_{m-1}(k).

1, 5, 47, 638, 11274, 245004, 6314664, 188204400, 6366517200, 240947474400, 10086271796160, 462688566802560, 23080457713017600, 1243853764482470400, 72018614888670643200, 4458392682933188966400, 293860908364035250022400, 20545850809171272549888000, 1518779004111434057997312000

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

a(1) = 1; a(n) = a(n-1)*2*(2n-1) - (2n-3)!/(n-1)!.

a(n) = (2*n)!/(4*n!)*(Psi(n+1/2) - Psi(n) + 2*log(2)). - Vladeta Jovovic, Jan 22 2005

E.g.f.: log((sqrt(1-4*x)+1)/2)*(2*x-sqrt(1-4*x)-1)/(-4*x+sqrt(1-4*x)+1). - Vladimir Kruchinin, Mar 17 2016

a(n) = n!*Sum_{k=1..n} (binomial(2*n-k-1,n-k)/k). - Vladimir Kruchinin, Mar 17 2016

a(n) ~ log(2) * 2^(2*n - 1/2) * n^n / exp(n). - Vaclav Kotesovec, Mar 17 2016

a(n) = n! * [x^n] -log(1 - x)/(1 - x)^n. - Ilya Gutkovskiy, Sep 21 2017

Example

a(3) = 3! (1 +(1 +(1 +1/2)) +(1 +(1 +1/2) +(1 +1/2 +1/3))) = 47.

Mathematica

Table[n! Sum[Binomial[2 n - k - 1, n - k]/k, {k, n}], {n, 19}] (* Michael De Vlieger, Mar 17 2016 *)

Prog

(Maxima)
a(n):=n!*sum(binomial(2*n-k-1, n-k)/k, k, 1, n);
/* Vladimir Kruchinin, Mar 17 2016 */
(PARI) lista(nn) = {print1(a=1, ", "); for (n=2, nn, a = a*2*(2*n-1) - (2*n-3)!/(n-1)!; print1(a, ", "); ); } \\ Michel Marcus, Mar 17 2016

Crossrefs

Cf. A000108.

Sequence in context: A370100 A328032 A074192 * A302616 A006902 A367079

Adjacent sequences: A058803 A058804 A058805 * A058807 A058808 A058809

Keyword

easy,nonn

Author

Leroy Quet, Jan 02 2001

Extensions

More terms from Michael De Vlieger, Mar 17 2016

Status

approved