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 A181078 G.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^(n+k-1) *x^k ] *x^n/n ). 3
 1, 1, 2, 5, 29, 657, 61207, 22168009, 29875987984, 155804714312491, 3016989471632014921, 229552430038667549657248, 64995077386747098368845127628, 73163996832774559516266954450479682 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Conjecture: this sequence consists entirely of integers. LINKS EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 29*x^4 + 657*x^5 + 61207*x^6 +... The logarithm begins: log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 95*x^4/4 + 3126*x^5/5 + 363132*x^6/6 +...+ A181079(n)*x^n/n +... which equals the series: log(A(x)) = (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 +...)*x + (1 + 2^2*x + 3^3*x^2 + 4^4*x^3 + 5^5*x^4 + 6^6*x^5 +...)*x^2/2 + (1 + 3^3*x + 6^4*x^2 + 10^5*x^3 + 15^6*x^4 + 21^7*x^5 +...)*x^3/3 + (1 + 4^4*x + 10^5*x^2 + 20^6*x^3 + 35^7*x^4 + 56^8*x^5 +...)*x^4/4 + (1 + 5^5*x + 15^6*x^2 + 35^7*x^3 + 70^8*x^4 + 126^9*x^5 +...)*x^5/5 + (1 + 6^6*x + 21^7*x^2 + 56^8*x^3 + 126^9*x^4 + 252^10*x^5 +...)*x^6/6 + (1 + 7^7*x + 28^8*x^2 + 84^9*x^3 + 210^10*x^4 + 462^11*x^5 +...)*x^7/7 +... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, n, binomial(m+k-1, k)^(m+k-1)*x^k)*x^m/m)+x*O(x^n)), n)} CROSSREFS Cf. A181079 (log), variants: A181074, A181076, A181070. Sequence in context: A098026 A179823 A064098 * A265773 A098717 A059784 Adjacent sequences:  A181075 A181076 A181077 * A181079 A181080 A181081 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 03 2010 STATUS approved

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Last modified September 26 09:44 EDT 2020. Contains 337346 sequences. (Running on oeis4.)