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 A258899 E.g.f.: 2 - exp(2) + Sum_{n>=1} 2^n * exp(x^n) / n!. 3

%I #6 Jun 20 2015 00:18:14

%S 1,2,6,10,42,34,786,130,17058,81154,545346,2050,102457218,8194,

%T 1141636866,72648608770,648648065538,131074,111258180895746,524290,

%U 40892974286411778,229774078552113154,28890711351291906,8388610,3552178288049960329218,34469355651846669074434

%N E.g.f.: 2 - exp(2) + Sum_{n>=1} 2^n * exp(x^n) / n!.

%H Paul D. Hanna, <a href="/A258899/b258899.txt">Table of n, a(n) for n = 0..500</a>

%F E.g.f.: 2 - exp(1) + Sum_{n>=1} exp(2*x^n) / n!.

%e E.g.f.: A(x) = 1 + 2*x + 6*x^2/2! + 10*x^3/3! + 42*x^4/4! + 34*x^5/5! + 786*x^6/6! +...

%e where

%e A(x) = 2 - exp(2) + 2*exp(x) + 2^2*exp(x^2)/2! + 2^3*exp(x^3)/3! + 2^4*exp(x^4)/4! + 2^5*exp(x^5)/5! +...

%e A(x) = 2 - exp(1) + exp(2*x) + exp(2*x^2)/2! + exp(2*x^3)/3! + exp(2*x^4)/4! + exp(2*x^5)/5! +...

%o (PARI) {a(n) = local(A=1); A = 2-exp(2) + sum(m=1,n,2^m/m!*exp(x^m +x*O(x^n))); if(n==0,1, n!*polcoeff(A,n))}

%o for(n=0,30, print1(a(n),", "))

%o (PARI) {a(n) = local(A=1); A = 2-exp(1) + sum(m=1,n,1/m!*exp(2*x^m +x*O(x^n))); if(n==0,1, n!*polcoeff(A,n))}

%o for(n=0,30, print1(a(n),", "))

%Y Cf. A258903.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 20 2015

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Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)