6,2

Let P(n+4,X)=(X+1)(X+2)(X+3)...(X+n+4); then a(n) is the coefficient of X^5; or a(n)=P'''''(n+4,0)/5! - Benoit Cloitre (benoit7848c(AT)orange.fr), May 09 2002

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.

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 226.

T. D. Noe, Table of n, a(n) for n=6..100

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].

Zerinvary Lajos, Sage Notebooks

E.g.f.: (-log(1-x))^6 or (1-x)^-1 * (-log(1-x))^5.

a(n) is coefficient of x^(n+6) in (-log(1-x))^6, multiplied by (n+6)!/6!.

(-log(1-x))^6 = x^6 + 3*x^7 + 23/4*x^8 + 9*x^9 + ...

(PARI) for(n=5, 50, print1(polcoeff(prod(i=1, n, x+i), 5, x), ", "))

sage: [stirling_number1(i, 6) for i in xrange(6, 22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008

Cf. A000254, A000399, A000454, A000482, A008275 (Stirling1 triangle).

Sequence in context: A036737 A141267 A016262 this_sequence A016260 A011810 A091947

Adjacent sequences: A001230 A001231 A001232 this_sequence A001234 A001235 A001236

nonn

njas