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 A062192 Row sums of unsigned triangle A062138 (generalized a=5 Laguerre). 6

%I

%S 1,7,57,529,5509,63591,805597,11109337,165625929,2654025319,

%T 45481765921,829903882017,16062421776397,328634683136839,

%U 7086337847838789,160604998959958441,3816483607166825617

%N Row sums of unsigned triangle A062138 (generalized a=5 Laguerre).

%H Seiichi Manyama, <a href="/A062192/b062192.txt">Table of n, a(n) for n = 0..441</a> (terms 0..100 from Harry J. Smith)

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

%F E.g.f.: exp(x/(1-x))/(1-x)^6.

%F a(n) = Sum_{m=0..n} n!*binomial(n+5, n-m)/m!.

%F a(n) = (2*n+5)*a(n-1) - (n-1)*(n+4)*a(n-2). - _Vaclav Kotesovec_, Oct 11 2012

%F a(n) ~ exp(2*sqrt(n)-n-1/2)*n^(n+11/4)/sqrt(2). - _Vaclav Kotesovec_, Oct 11 2012

%t Table[Sum[n! Binomial[n+5,n-m]/m!,{m,0,n}],{n,0,20}] (* _Harvey P. Dale_, Apr 11 2012 *)

%o (PARI) { f=1; for (n=0, 100, if (n>1, f*=n); a=f*binomial(n+5, n); g=1; a+=sum(m=1, n, f*binomial(n+5, n-m)/g*=m); write("b062192.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 02 2009

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(x/(1-x))/(1-x)^6)) \\ _G. C. Greubel_, Feb 06 2018

%o (MAGMA) [Factorial(n)*(&+[Binomial(n+5,n-m)/Factorial(m): m in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Feb 06 2018

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 19 2001

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Last modified February 22 18:24 EST 2020. Contains 332148 sequences. (Running on oeis4.)