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A258899 E.g.f.: 2 - exp(2) + Sum_{n>=1} 2^n * exp(x^n) / n!. 3
1, 2, 6, 10, 42, 34, 786, 130, 17058, 81154, 545346, 2050, 102457218, 8194, 1141636866, 72648608770, 648648065538, 131074, 111258180895746, 524290, 40892974286411778, 229774078552113154, 28890711351291906, 8388610, 3552178288049960329218, 34469355651846669074434 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..500

FORMULA

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

EXAMPLE

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! +...

where

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! +...

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! +...

PROG

(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))}

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

(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))}

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

CROSSREFS

Cf. A258903.

Sequence in context: A111414 A202533 A275700 * A248784 A067868 A298760

Adjacent sequences:  A258896 A258897 A258898 * A258900 A258901 A258902

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 20 2015

STATUS

approved

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Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)