5,2

Let P(n+3,X)=(X+1)(X+2)(X+3)...(X+n+3); then a(n) is the coefficient of X^4; or a(n)=P''''(n+3,0)/4! - 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=5..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))^5 or (1-x)^-1 * (-log(1-x))^4

a(n) is coefficient of x^(n+5) in (-log(1-x))^5, multiplied by (n+5)!/5!

(-log(1-x))^5 = x^5 + 5/2*x^6 + 25/6*x^7 + 35/6*x^8 + ...

(PARI) for(n=4, 50, print1(polcoeff(prod(i=1, n, x+i), 4, x), ", "))

sage: [stirling_number1(i, 5) for i in xrange(5, 22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008

Cf. A000254, A000399, A000454, A001233, A008275 (Stirling1 triangle).

Sequence in context: A036083 A051588 A016164 this_sequence A069379 A120995 A024197

Adjacent sequences: A000479 A000480 A000481 this_sequence A000483 A000484 A000485

nonn

njas