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A078945
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Row sums of A078939, the fourth power of lower triangular matrix A056857.
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17
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1, 5, 29, 189, 1357, 10589, 88909, 797085, 7583373, 76179037, 804638925, 8904557341, 102929260813, 1239432543709, 15511264432973, 201330839371421, 2705249923950477, 37567754666530141, 538369104335121869
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| E.g.f.: exp{4(e^x-1)+x}.
Stirling transform of [1, 4, 4^2, 4^3, ...]. - 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^{-4}*f_n(4). - Milan R. Janjic (agnus(AT)blic.net), May 30 2008
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MAPLE
| A078945 := 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=4, %), 66)) end:
seq(A078945(n), n=0..18); # - Peter Luschny, Mar 30 2011
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MATHEMATICA
| Table[n!, {n, 0, 20}]CoefficientList[Series[E^(4E^x-4+x), {x, 0, 20}], x]
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CROSSREFS
| Cf. A078939, A078944, A000110, A035009, A078940.
Equals A078944(n+1)/4.
Sequence in context: A059231 A127846 A137573 * A113713 A142980 A062191
Adjacent sequences: A078942 A078943 A078944 * A078946 A078947 A078948
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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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