%I A053567
%S A053567 120,1764,13132,67284,269325,902055,2637558,6926634,16669653,
%T A053567 37312275,78558480,156952432,299650806,549789282,973941900,
%U A053567 1672280820,2792167686,4546047198,7234669596,11276842500
%V A053567 -120,1764,-13132,67284,-269325,902055,-2637558,6926634,-16669653,
%W A053567 37312275,-78558480,156952432,-299650806,549789282,-973941900,
%X A053567 1672280820,-2792167686,4546047198,-7234669596,11276842500
%N A053567 Stirling numbers of first kind.
%D A053567 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions,
National Bureau of Standards Applied Math. Series 55, 1964 (and various
reprintings), p. 833.
%H A053567 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National
Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972
[alternative scanned copy].
%F A053567 a(n)=(-1)^n*binomial(n+5, 6)*binomial(n+5, 2)*(3*n^2+23*n+38)/8.
%F A053567 G.f.: x*(120+444*x+328*x^2+52*x^3+x^4)/(1-x)^11. See row k=4 of triangle
A112007 for the coefficients.
%F A053567 E.g.f. with offset 5: exp(x)*(sum(A112486(5, m)*(x^(5+m))/(5+m)!, m=0..5)).
%F A053567 a(n)= binomial(n+5, 6)*binomial(n+5, 2)*(3*n^2+23*n+38)/8. From the g.f.
%F A053567 a(n)= (f(n+4, 5)/10!)*sum(A112486(5, m)*f(10, 5-m)*f(n-1, m), m=0..min(5,
n-1)), with the falling factorials f(n, m):=n*(n-1)*, ..., *(n-(m-1)).
From the e.g.f.
%o A053567 (Other) sage: [stirling_number1(n,n-5)*(-1)^(n+1) for n in xrange(6,
26)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16
2009]
%Y A053567 Next |Stirling1| diagonal A112002.
%Y A053567 Sequence in context: A052776 A052770 A027795 this_sequence A056270 A001118
A052767
%Y A053567 Adjacent sequences: A053564 A053565 A053566 this_sequence A053568 A053569
A053570
%K A053567 easy,sign
%O A053567 1,1
%A A053567 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000
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