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A078945 Row sums of A078939, the fourth power of lower triangular matrix A056857. 17
1, 5, 29, 189, 1357, 10589, 88909, 797085, 7583373, 76179037, 804638925, 8904557341, 102929260813, 1239432543709, 15511264432973, 201330839371421, 2705249923950477, 37567754666530141, 538369104335121869 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals A078944(n+1)/4.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

E.g.f.: exp{4(e^x-1)+x}.

Stirling transform of [1, 4, 4^2, 4^3, ...]. - Gerald McGarvey, Jun 01 2005

Define f_1(x), f_2(x), ... such that f_1(x)=e^x, f_{n+1}(x) = (d/dx)(x*f_n(x)), for n=2,3,.... Then a(n)=e^{-4}*f_n(4). - Milan Janjic, May 30 2008

G.f.: 1/(Q(0) - 4*x) where Q(k) =  1 - x*(k+1)/( 1 - 4*x/Q(k+1) ); (continued fraction ). - Sergei N. Gladkovskii, Mar 22 2013

G.f.: T(0)/(1-5*x), where T(k) = 1 - 4*x^2*(k+1)/( 4*x^2*(k+1) - (1-5*x-x*k)*(1-6*x-x*k)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 28 2013

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

MATHEMATICA

Table[n!, {n, 0, 20}]CoefficientList[Series[E^(4E^x-4+x), {x, 0, 20}], x]

Table[1/E^4/4*Sum[m^n/m!*4^m, {m, 0, Infinity}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 12 2014 *)

CROSSREFS

Cf. A078939, A078944, A000110, A035009, A078940.

Sequence in context: A059231 A137573 A234317 * A113713 A142980 A062191

Adjacent sequences:  A078942 A078943 A078944 * A078946 A078947 A078948

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 18 2002

EXTENSIONS

More terms from Robert G. Wilson v, Dec 19 2002

STATUS

approved

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Last modified October 20 21:25 EDT 2019. Contains 328273 sequences. (Running on oeis4.)