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.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd. ed., 1994, p. 259.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 48.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
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].
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = binomial(n+4, 5)*(15*n^3 + 150*n^2 + 485*n + 502)/48. - André F. Labossière, Sep 30 2004
Stirling1(n+1, n-3) = Sum_{L=1..n} (Sum_{k=L+1..n} (Sum_{j=k+1..n} (Sum_{i=j+1..n} i*j*k*L))), cf. A001298. - Vladeta Jovovic, Jan 31 2005
E.g.f. with offset 4: exp(x)*(Sum_{m=0..4} A112486(4,m)*(x^(4+m))/(4+m)!).
a(n) = (f(n+3, 4)/8!)*Sum_{m=0..min(4, n-1)} A112486(4,m)*f(8, 4-m)*f(n-1, m), 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].
a(n) = A001298(-4-n) for all n in Z. - Michael Somos, Sep 04 2017
MAPLE
A000915 := proc(n)
combinat[stirling1](n+4, n) ;
end proc:
seq(A000915(n), n=1..10) ; # R. J. Mathar, May 19 2016
MATHEMATICA
Table[Binomial[n + 4, 5]*(15*n^3 + 150*n^2 + 485*n + 502)/48, {n, 50}] (* T. D. Noe, Jun 20 2012 *)
a[ n_] := n (n + 1) (n + 2) (n + 3) (n + 4) (15 n^3 + 150 n^2 + 485 n + 502) / 5760; (* Michael Somos, Sep 04 2017 *)
PROG
(PARI) {a(n) = n * (n+1) * (n+2) * (n+3) * (n+4) * (15*n^3+ 150*n^2 + 485*n + 502) / 5760}; /* Michael Somos, Sep 04 2017 */
(Sage) [stirling_number1(n, n-4) for n in range(5, 30)] # Zerinvary Lajos, May 16 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000
STATUS
approved