4,2

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.

C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 519.

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 sequences related to Laguerre polynomials

a(n) = n!*n*(n-1)(n-2)(n-3)/(4!)^2. a(4)=1, a(n+1)=a(n) * (n+1)^2 / (n-3).

a(n)=A021009(n, 4), n >= 4. E.g.f.: x^4/(4!*(1-x)^5).

If we define f(n,i,x)= sum(sum(binomial(k,j)*stirling1(n,k)*stirling2(j,i)*x^(k-j),j=i..k),k=i..n) then a(n)=(-1)^n*f(n,4,-5), (n>=4). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]

with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r+2), right=Set(U, card<r), U=Sequence(Z, card>=1)}, labeled]: subs(r=2, stack): seq(count(subs(r=2, ZL), size=m), m=4..19) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 07 2008

sage: [factorial(m)*binomial(m, 4)/24 for m in xrange (4, 19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 05 2008

Cf. A053495.

Sequence in context: A018207 A001714 A016633 this_sequence A131279 A056069 A089386

Adjacent sequences: A001808 A001809 A001810 this_sequence A001812 A001813 A001814

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Larry Reeves (larryr(AT)acm.org), Feb 07 2001