A074932 Row sums of unsigned triangle A075513.

1, 3, 18, 170, 2200, 36232, 725200, 17095248, 463936896, 14246942336, 488428297984, 18491942300416, 766293946203136, 34498781924766720, 1676731077272217600, 87501958444207351808, 4880017252828686155776

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Victor J. W. Guo, Yiting Yang, Proof of a conjecture of Kløve on permutation codes under the Chebychev distance, arXiv:1704.01295 [cs.IT], 2017. Also in Designs, Codes and Cryptography, June 2017, Volume 83, Issue 3, pp 685-690.

Torleiv Kløve, Spheres of Permutations under the Infinity Norm - Permutations with limited displacement, Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.

Formula

a(n) = sum(|A075513(n, m)|, m=0..n-1) = sum(binomial(n-1, m)*(m+1)^(n-1), m=0..n-1), n>=1.

E.g.f.: log(G(x)) where G(x) = (1 + exp(2*x*G(x)))/2 is the e.g.f. of A201595. - Paul D. Hanna, Aug 02 2012

E.g.f: log(x-LambertW(-x*exp(x)))-log(2*x). - Vaclav Kotesovec, Dec 04 2012

a(n) ~ n!/(sqrt(2*Pi*(1+LambertW(exp(-1))))*n^(3/2)*LambertW(exp(-1))^n). - Vaclav Kotesovec, Dec 04 2012

a(n) = A072034(n)/n. - Vladimir Reshetnikov, Nov 09 2016

O.g.f.: Sum_{k>=1} k^(k-1)*x^k/(1 - k*x)^k. - Ilya Gutkovskiy, Oct 09 2018

Example

E.g.f.: A(x) = x + 3*x^2/2! + 18*x^3/3! + 170*x^4/4! + 2200*x^5/5! +...
where exp(A(x)) = 1 + x + 4*x^2/2! + 28*x^3/3! + 288*x^4/4! + 3936*x^5/5! + 67328*x^6/6! +...+ A201595(n)*x^n/n! +...

Mathematica

Rest[CoefficientList[Series[Log[x-LambertW[-x*Exp[x]]]-Log[2*x], {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Dec 04 2012 *)
a[n_] := Sum[Binomial[n-1, k]*(k+1)^(n-1), {k, 0, n-1}]; Table[a[n], {n, 1, 17}] (* Jean-François Alcover, Jul 09 2013, after Paul D. Hanna *)

Prog

(PARI) {a(n)=sum(k=0, n-1, binomial(n-1, k)*(k+1)^(n-1))} \\ Paul D. Hanna, Aug 02 2012
(PARI) {a(n)=local(A201595=serreverse(x-x*tanh(x+x^2*O(x^n)))/x); n!*polcoeff(log(A201595), n)} \\ Paul D. Hanna, Aug 02 2012
(PARI) {a(n) = my(A); if( n<0, 0, A = O(x); for(k=1, n, A = log( (1 + exp( 2*x * exp(A))) / 2 )); n! * polcoeff(A, n))}; /* Michael Somos, Apr 10 2018 */

Crossrefs

Cf. A201595.

Sequence in context: A052668 A224788 A121423 * A101483 A234302 A099716

Adjacent sequences: A074929 A074930 A074931 * A074933 A074934 A074935

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved