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A244822
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E.g.f.: Sum_{n>=0} exp(n*4^n*x) * x^n/n!.
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4
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1, 1, 9, 145, 7169, 702721, 173051905, 86399717377, 99140462706689, 233906591488868353, 1206701231035902853121, 12911553576265127971258369, 292981931017250265780757463041, 13856406784814016950200694583853057, 1362697700959059311763086710096185524225
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OFFSET
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0,3
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LINKS
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FORMULA
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O.g.f.: Sum_{n>=0} x^n/(1 - n*4^n*x)^(n+1).
a(n) = Sum_{k=0..n} C(n,k) * k^(n-k) * 4^(k*(n-k)).
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 9*x^2/2! + 145*x^3/3! + 7169*x^4/4! + 702721*x^5/5! +...
where
A(x) = 1 + exp(4*x)*x + exp(4^2*x)^2*x^2/2! + exp(4^3*x)^3*x^3/3! + exp(4^4*x)^4*x^4/4! + exp(4^5*x)^5*x^5/5! + exp(4^6*x)^6*x^6/6! +...
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MATHEMATICA
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Flatten[{1, Table[Sum[Binomial[n, k]*k^(n-k)*4^(k*(n-k)), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jul 11 2014 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, binomial(n, k) * k^(n-k) * 4^(k*(n-k)) )}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(k*4^k*x +x*O(x^n))*x^k/k!), n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1-k*4^k*x +x*O(x^n))^(k+1)), n)}
for(n=0, 25, print1(a(n), ", "))
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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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