A118795 E.g.f.: -1 + exp(( 1 - sqrt(5 - 4*exp(x)) )/2).
0, 1, 4, 29, 329, 5172, 104335, 2571473, 74894818, 2516911731, 95862252417, 4080739041238, 192000366357981, 9894168501171229, 554208686184384028, 33527021385789228265, 2178482569432714859789, 151314182463701892157460, 11188187745418763137485747
Offset: 0
Keywords
Examples
E.g.f.: A(x) = x + (4/2)*x^2 + (29/6)*x^3 + (329/24)*x^4 + (5172/120)*x^5 + ...
Programs
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Mathematica
CoefficientList[Series[-1 + E^((1-Sqrt[5-4*E^x])/2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 14 2014 *) -
Maxima
a(n):=sum((sum(((i+k-1)!*binomial(k+2*i-1,i+k-1)*stirling2(n,i+k)), i,0,n-k))/(k-1)!,k,1,n); /* Vladimir Kruchinin, Nov 22 2011 */
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PARI
a(n)=local(x=X+X^2*O(X^n));n!*polcoeff(-1+exp((1-sqrt(5-4*exp(x)))/2),n,X)
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PARI
/* As the unsigned row sums of A118793: */ a(n)=local(x=X+X^2*O(X^n));if(n<1,0, (n-1)!*sum(k=0,n-1,abs(polcoeff(((x/log(1-x-x^2)))^n/(n-1-k)!,k,X))))
Formula
a(n) = (n-1)!*Sum_{k=0..n-1} abs( [x^k] (x/log(1-x-x^2))^n/(n-1-k)! ) for n>0.
a(n) = sum(k=1..n, (sum(i=0..n-k, ((i+k-1)!*C(k+2*i-1,i+k-1) *stirling2(n, i+k))))/(k-1)!). - Vladimir Kruchinin, Nov 22 2011
a(n) ~ sqrt(5) * n^(n-1) / (2^(3/2) * exp(n-1/2) * (log(5/4))^(n-1/2)). - Vaclav Kotesovec, Jul 14 2014
Comments