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 A172389 a(n) = Sum_{k=0..n} C(n,k)*3^(k*(n-k))/2^n. 1
 1, 1, 2, 7, 44, 481, 9272, 310087, 18164624, 1843946881, 326808099872, 100310221406407, 53656068398769344, 49686835289802328801, 80090696216400251499392, 223445962168511596412895367 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..15. FORMULA O.g.f.: A(x) = Sum_{n>=0} 2*x^n/(2 - 3^n*x)^(n+1). E.g.f.: E(x) = Sum_{n>=0} exp(3^n*x/2)*(x/2)^n/n!. a(n) = A135079(n)/2^n. EXAMPLE O.g.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 481*x^5 + 9272*x^6 +... A(x) = 2/(2-x) + 2*x/(2-3*x)^2 + 2*x^2/(2-3^2*x)^3 + 2*x^3/(2-3^3*x)^4 +...+ 2*x^n/(2-3^n*x)^(n+1) +... E.g.f.: E(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 44*x^4/4! + 481*x^5/5! +... E(x) = exp(x/2) + exp(3*x/2)*x/2 + exp(3^2*x/2)*(x/2)^2/2! + exp(3^3*x/2)*(x/2)^3/3! +...+ exp(3^n*x/2)*(x/2)^n/n! +... PROG (PARI) {a(n)=sum(k=0, n, binomial(n, k)*3^(k*(n-k)))/2^n} (PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(3^k*x/2 +x*O(x^n))*(x/2)^k/k!), n)} (PARI) {a(n)=polcoeff(sum(k=0, n, (x/2)^k/(1-3^k*x/2 +x*O(x^n))^(k+1)), n)} CROSSREFS Cf. variants: A135079, A047863. Sequence in context: A001046 A158257 A348857 * A153522 A355109 A278295 Adjacent sequences: A172386 A172387 A172388 * A172390 A172391 A172392 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 03 2010 STATUS approved

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Last modified April 14 05:31 EDT 2024. Contains 371655 sequences. (Running on oeis4.)