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A052780
Expansion of e.g.f. x^2*exp(4*x).
2
0, 0, 2, 24, 192, 1280, 7680, 43008, 229376, 1179648, 5898240, 28835840, 138412032, 654311424, 3053453312, 14092861440, 64424509440, 292057776128, 1314259992576, 5875515260928, 26113401159680
OFFSET
0,3
COMMENTS
Old name was: A simple grammar.
FORMULA
E.g.f.: x^2*exp(x)^4.
a(n) = 2*A038845(n-2).
Recurrence: a(1)=0, a(2)=2, (n-1)*a(n+1) - 4*(n+1)*a(n) = 0.
From Ralf Stephan, Mar 26 2003: (Start)
a(n) = n*(n-1)*4^(n-2).
G.f.: 2*x^2/(1-4*x)^3. (End)
MAPLE
spec := [S, {B=Set(Z), S=Prod(Z, Z, B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
seq(n*(n-1)*4^(n-2), n=0..20); # Zerinvary Lajos, Apr 25 2007
MATHEMATICA
Table[4^(n-2)*n*(n-1), {n, 0, 30}] (* G. C. Greubel, Jul 20 2019 *)
With[{nn=20}, CoefficientList[Series[x^2 Exp[4x], {x, 0, nn}], x] Range[0, nn]!] (* or *) LinearRecurrence[{12, -48, 64}, {0, 0, 2}, 30] (* Harvey P. Dale, Sep 28 2022 *)
PROG
(PARI) vector(30, n, n--; 4^(n-2)*n*(n-1)) \\ G. C. Greubel, Jul 20 2019
(Magma) [4^(n-2)*n*(n-1): n in [0..30]]; // G. C. Greubel, Jul 20 2019
(Sage) [4^(n-2)*n*(n-1) for n in (0..30)] # G. C. Greubel, Jul 20 2019
(GAP) List([0..30], n-> 4^(n-2)*n*(n-1)); # G. C. Greubel, Jul 20 2019
CROSSREFS
Cf. A038845.
Sequence in context: A059387 A126190 A121356 * A245019 A189769 A208533
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name from e.g.f. by Jon E. Schoenfield, Feb 07 2019
STATUS
approved