A384820 G.f. A(x) = exp( Sum_{n>=1} (n^2 - A384819(n))*x^n/n ) where A384819(k) < k for k >= 1 such that A(x) is a power series with integral coefficients.
1, 1, 2, 4, 8, 14, 25, 43, 74, 124, 205, 335, 543, 869, 1379, 2170, 3388, 5249, 8079, 12353, 18776, 28375, 42651, 63782, 94923, 140614, 207384, 304578, 445528, 649200, 942495, 1363447, 1965697, 2824676, 4046190, 5778273, 8227533, 11681632, 16540183, 23357053, 32898242
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 8*x^4 + 14*x^5 + 25*x^6 + 43*x^7 + 74*x^8 + 124*x^9 + 205*x^10 + 335*x^11 + 543*x^12 + 869*x^13 + 1379*x^14 + 2170*x^15 + 3388*x^16 + ... where log(A(x)) = x/(1-x)^2 - D(x) and D(x) is the l.g.f. of A384819: D(x) = 0*x + 1*x^2/2 + 2*x^3/3 + 1*x^4/4 + 4*x^5/5 + 3*x^6/6 + 6*x^7/7 + 1*x^8/8 + 2*x^9/9 + 7*x^10/10 + 10*x^11/11 + 3*x^12/12 + 12*x^13/13 + 11*x^14/14 + 3*x^15/15 + 1*x^16/16 + ... + A384819(n)*x^n/n + ...
Links
- Paul D. Hanna, Table of n, a(n) for n = 0..520
Programs
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PARI
{a(n) = my(L=[1],A=1); for(i=1,n, L = concat(L,t); for(t=1,(#L)^2+1, if( denominator( eval(polcoef( A = exp( intformal(Ser(L)) ),#L)) )==1, L[#L] = t + (#L)*(#L-1); break)) ); polcoef(A,n)} for(n=0,40, print1(a(n),", "))