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A195509
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Expansion of e.g.f. (exp(x*exp(x)) + exp(x/exp(x)))/2.
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1
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1, 1, 1, 4, 25, 96, 481, 3368, 20721, 141760, 1146721, 9098112, 77652169, 726208640, 6891125697, 69344336896, 738718169569, 8076031881216, 92647353941569, 1106883171037184, 13616813607795321, 174298975125127168, 2304515271134124577
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: Sum_{n>=0} x^n*cosh(n*x)/n!.
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EXAMPLE
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E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 25*x^4/4! + 96*x^5/5! + 481*x^6/6! +...
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MAPLE
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a := proc(n) local m: add(binomial(n, 2*m)*(n - 2*m)^(2*m), m = 0 .. floor(1/2*n - 1/2)): end proc:
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PROG
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(PARI) {a(n)=local(X=x+x*O(x^n), A=1+X); A=(exp(X*exp(X))+exp(X/exp(X)))/2; n!*polcoeff(A, n)}
(PARI) {a(n)=n!*polcoeff(sum(m=0, n, x^m*cosh(m*x+x*O(x^n))/m!), n)}
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^(2*k)*binomial(n, 2*k)); \\ Seiichi Manyama, Feb 15 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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