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A062148 Second (unsigned) column sequence of triangle A062138 (generalized a=5 Laguerre). 6

%I

%S 1,14,168,2016,25200,332640,4656960,69189120,1089728640,18162144000,

%T 319653734400,5928123801600,115598414131200,2365321396838400,

%U 50685458503680000,1135354270482432000

%N Second (unsigned) column sequence of triangle A062138 (generalized a=5 Laguerre).

%H Indranil Ghosh, <a href="/A062148/b062148.txt">Table of n, a(n) for n = 0..400</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>

%F E.g.f.: (1+6*x)/(1-x)^8.

%F a(n) = A062138(n+1, 1) = (n+1)!*binomial(n+6, 6).

%F If we define f(n,i,x)= Sum_{k=i..n}(Sum_{j=i..k}(binomial(k,j) *Stirling1(n,k)* Stirling2(j,i)*x^(k-j))) then a(n-1) = (-1)^(n-1) * f(n,1,-7), (n>=1). - _Milan Janjic_, Mar 01 2009

%F Assuming offset 1: a(n) = n!*binomial(-n,6). - _Peter Luschny_, Apr 29 2016

%e a(3) = (3+1)! * binomial(3+6,6) = 24 * 84 = 2016. - _Indranil Ghosh_, Feb 24 2017

%t Table[Sum[n!/6!, {i, 6, n}], {n, 6, 21}] (* _Zerinvary Lajos_, Jul 12 2009 *)

%o (PARI) a(n)=(n+1)!*binomial(n+6,6) \\ _Indranil Ghosh_, Feb 24 2017

%o (Python)

%o import math

%o f=math.factorial

%o def C(n,r):return f(n)/f(r)/f(n-r)

%o def A062148(n): return f(n+1)*C(n+6,6) # _Indranil Ghosh_, Feb 24 2017

%o (MAGMA) [Factorial(n+1)*Binomial(n+6,6): n in [0..30]]; // _G. C. Greubel_, Feb 06 2018

%Y Cf. A001725 (first column of A062138).

%Y Appears in the third left hand column of A167556 multiplied by 120. - _Johannes W. Meijer_, Nov 12 2009

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 19 2001

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)