1,1

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.

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].

a(n)=(-1)^n*binomial(n+5, 6)*binomial(n+5, 2)*(3*n^2+23*n+38)/8.

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.

E.g.f. with offset 5: exp(x)*(sum(A112486(5, m)*(x^(5+m))/(5+m)!, m=0..5)).

a(n)= binomial(n+5, 6)*binomial(n+5, 2)*(3*n^2+23*n+38)/8. From the g.f.

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.

(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]

Next |Stirling1| diagonal A112002.

Sequence in context: A052776 A052770 A027795 this_sequence A056270 A001118 A052767

Adjacent sequences: A053564 A053565 A053566 this_sequence A053568 A053569 A053570

easy,sign

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000