Search: id:A053567 Results 1-1 of 1 results found. %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., Handbook of Mathematical Functions, 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 Search completed in 0.001 seconds