|
Search: id:A000915
|
|
|
| A000915 |
|
Stirling numbers of first kind s(n,n-4).
(Formerly M5155 N2239)
|
|
+0
4
|
|
| 24, 274, 1624, 6769, 22449, 63273, 157773, 357423, 749463, 1474473, 2749747, 4899622, 8394022, 13896582, 22323822, 34916946, 53327946, 79721796, 116896626, 168423871, 238810495, 333685495, 460012995, 626334345, 843041745
(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.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 227, #16.
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 226.
|
|
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].
A. F. Labossiere, Sobalian Coefficients.
A. F. Labossiere, Miscellaneous.
|
|
FORMULA
|
a(n) = binomial(n+4, 5)*(15*n^3+150*n^2+485*n+502)/48 - Andre F. Labossiere (boronali(AT)laposte.net), Sep 30 2004
Stirling1(n+1, n-3) = Sum(Sum(Sum(Sum(i*j*k*l, i = j+1 .. n), j = k+1 .. n), k = l+1 .. n), l = 1 .. n), cf. A001298. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 31 2005
E.g.f. with offset 4: exp(x)*(sum(A112486(4, m)*(x^(4+m))/(4+m)!, m=0..4)).
a(n)= (f(n+3, 4)/8!)*sum(A112486(4, m)*f(8, 4-m)*f(n-1, m), m=0..min(4, n-1)), with the falling factorials f(n, m):=n*(n-1)*...*(n-(m-1)).
G.f.: x*(24+58*x+22*x^2+x^3)/(1-x)^9, see the k=3 row of triangle A112007 for [24, 58, 22, 1].
|
|
CROSSREFS
|
Cf. A094216.
Adjacent sequences: A000912 A000913 A000914 this_sequence A000916 A000917 A000918
Sequence in context: A022065 A125412 A062027 this_sequence A006665 A010940 A045854
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000
|
|
|
Search completed in 0.005 seconds
|
