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A078940
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Row sums of A078938, the cube of lower triangular matrix A056857.
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4
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1, 4, 19, 103, 622, 4117, 29521, 227290, 1865881, 16239523, 149142952, 1439618143, 14555631781, 153700654036, 1690684883191, 19328770917499, 229203640111870, 2814018686591089, 35711716110387589, 467766675528462562
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Divide by 3^n and insert an initial 1 to get sequence that shifts left one place under 1/3 order binomial transformation. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 13 2006
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FORMULA
| E.g.f.: exp{3(e^x-1)+x}.
Stirling transform of [1, 3, 3^2, 3^3, ...]. - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Jun 01 2005
Define f_1(x),f_2(x),... such that f_1(x)=e^x, f_{n+1}(x)=diff(x*f_n(x),x), for n=2,3,.... Then a(n)=e^{-3}*f_n(3). - Milan R. Janjic (agnus(AT)blic.net), May 30 2008
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MAPLE
| A078940 := proc(n) local a, b, i;
a := [seq(2, i=1..n)]; b := [seq(1, i=1..n)];
exp(-x)*hypergeom(a, b, x); round(evalf(subs(x=3, %), 66)) end:
seq(A078940(n), n=0..19); # - Peter Luschny, Mar 30 2011
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MATHEMATICA
| Table[n!, {n, 0, 20}]CoefficientList[Series[E^(3E^x-3+x), {x, 0, 20}], x]
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CROSSREFS
| Cf. A078938, A035009, A078945.
Sequence in context: A151382 A188675 A199876 * A110531 A178302 A186997
Adjacent sequences: A078937 A078938 A078939 * A078941 A078942 A078943
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 18 2002
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 19 2002
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