3,2

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

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 217.

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=3..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].

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 32

E.g.f. (-log(1-x))^3 or (1-x)^-1 * (-log(1-x))^2.

a(n) is coefficient of x^(n+3) in (-log(1-x))^3, multiplied by (n+3)!/6.

[(sum(1/i, i=1..n-1)^2-sum(1/i^2, i=1..n-1)]*(n-1)!/2 -Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 18 2000

(-log(1-x))^3 = x^3 + 3/2*x^4 + 7/4*x^5 + 15/8*x^6 + ...

(MuPAD) f := proc(n) option remember; begin n^3*f(n-3)-(3*n^2+3*n+1)*f(n-2)+3*(n+1)*f(n-1) end_proc: f(0) := 1: f(1) := 6: f(2) := 35:

(PARI) for(n=2, 50, print1(polcoeff(prod(i=1, n, x+i), 2, x), ", "))

sage: [stirling_number1(i+2, 3) for i in xrange(1, 22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008

Cf. A000254, A000454, A000482, A001233, A008275 (Stirling1 triangle).

Adjacent sequences: A000396 A000397 A000398 this_sequence A000400 A000401 A000402

Sequence in context: A121838 A001109 A117671 this_sequence A081051 A087631 A030446

nonn,easy,nice

njas