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A074932 Row sums of unsigned triangle A075513. 3
1, 3, 18, 170, 2200, 36232, 725200, 17095248, 463936896, 14246942336, 488428297984, 18491942300416, 766293946203136, 34498781924766720, 1676731077272217600, 87501958444207351808, 4880017252828686155776 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)