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A090362
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Satisfies A^6 = BINOMIAL(A)^5 and also equals A090358^5.
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4
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1, 5, 40, 460, 7220, 148276, 3831760, 120333680, 4460572870, 190679906990, 9230084185456, 498734395394840, 29740372199558420, 1939241402832412180, 137222625361036807760, 10470376552560151801616, 856818090423771231257245
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: A(x)^6 = A(x/(1-x))^5/(1-x)^5.
O.g.f.: A(x) = exp( Sum_{n >= 1} b(n)*x^n/n ), where b(n) = Sum_{k = 1..n} k!*Stirling2(n,k)*5^k = A094418(n).
BINOMIAL(A(x)) = exp( Sum_{n >= 1} c(n)*x^n/n ) where c(n) = (-1)^n*Sum_{k = 1..n} k!*Stirling2(n,k)*(-6)^k. A(x) = B(x)^5 and BINOMIAL(A(x)) = B(x)^6 where B(x) = 1 + x + 6*x^2 + 66*x^3 + 1071*x^4 + ... is the o.g.f. for A090358. See also A019538. (End)
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MATHEMATICA
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nmax = 16; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[A[x]^6 - A[x/(1 - x)]^5/(1 - x)^5 + O[x]^(n + 1), x] == 0 /. sol; sol = sol ~Join~ Solve[eq][[1]], {n, 1, nmax}];
sol /. Rule -> Set;
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PROG
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(PARI) {a(n)=local(A); if(n<0, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A, x, x/(1-x))/(1-x)+x*O(x^n); A=A-A^6+B^5); polcoeff(A, n, x))}
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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