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A052790
Expansion of e.g.f.: x^2*log(1-x)^4.
1
0, 0, 0, 0, 0, 0, 720, 10080, 114240, 1270080, 14621040, 177629760, 2292618240, 31485168000, 459767275968, 7126635035520, 117007217832960, 2030137891891200, 37138576448883456, 714734162773420032, 14439823458634690560, 305638240397811793920, 6764967047810572812288
OFFSET
0,7
COMMENTS
Original name: a simple grammar.
LINKS
FORMULA
E.g.f.: x^2*log(-1/(-1+x))^4.
Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (32*n-464*n^2-21*n^6-22*n^5+48*n^3+n^8+2*n^7+384+160*n^4)*a(n) + (105*n^4-360-14*n^6-121*n^2-4*n^7+642*n-296*n^3+48*n^5)*a(n+1) + (-84*n+24*n^5+179*n^2+6*n^6-35*n^4-90*n^3)*a(n+2) + (14*n^2+12*n^3-8*n-14*n^4-4*n^5)*a(n+3) + (-n^2+n^4-2*n+2*n^3)*a(n+4)}.
a(n) = n*A052770(n-1) = 4!*n*(n-1)*abs(Stirling1(n-2,4)) for n >= 2. - Andrew Howroyd, Aug 08 2020
MAPLE
spec := [S, {B=Cycle(Z), S=Prod(Z, Z, B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[x^2 Log[-1/(x-1)]^4, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 28 2016 *)
PROG
(PARI) a(n)={if(n>=2, 4!*n*(n-1)*abs(stirling(n-2, 4, 1)), 0)} \\ Andrew Howroyd, Aug 08 2020
CROSSREFS
Sequence in context: A052786 A187192 A052792 * A052521 A213876 A052785
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
Name changed and terms a(20) and beyond from Andrew Howroyd, Aug 08 2020
STATUS
approved