|
Search: id:A053567
|
|
|
| A053567 |
|
Stirling numbers of first kind. |
|
+0
4
|
|
| -120, 1764, -13132, 67284, -269325, 902055, -2637558, 6926634, -16669653, 37312275, -78558480, 156952432, -299650806, 549789282, -973941900, 1672280820, -2792167686, 4546047198, -7234669596, 11276842500
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
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.
|
|
LINKS
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
|
|
FORMULA
|
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.
|
|
CROSSREFS
|
Next |Stirling1| diagonal A112002.
Adjacent sequences: A053564 A053565 A053566 this_sequence A053568 A053569 A053570
Sequence in context: A052776 A052770 A027795 this_sequence A056270 A001118 A052767
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000
|
|
|
Search completed in 0.002 seconds
|
