A144002
E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral 1/A(x)^2 dx ).
Original entry on oeis.org
1, 1, 2, 10, 88, 1152, 20448, 464608, 12998176, 435443328, 17106187520, 775347933312, 40025403691136, 2328514989726720, 151324140857050624, 10904257049278844416, 865717992565002800640, 75309304802558209263616, 7143418423952431605493760, 735668180680897524348745728
Offset: 0
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 10*x^3/3! + 88*x^4/4! + 1152*x^5/5! + ...
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{a(n) = my(A=1+x+x*O(x^n)); for(i=0,n, A = 1 + serreverse(intformal(1/A^2))); n!*polcoef(A,n)}
for(n=0,20,print1(a(n),", "))
A144003
E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral 1/A(x)^3 dx ).
Original entry on oeis.org
1, 1, 3, 24, 339, 7101, 200961, 7256277, 321662502, 17029233774, 1054682936433, 75199620036177, 6094256204678922, 555527437385512095, 56468189426338157580, 6353824422205136494044, 786458781488123265873519
Offset: 0
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 24*x^3/3! + 339*x^4/4! + 7101*x^5/5! + 200961*x^6/6! + 7256277*x^7/7! + 321662502*x^8/8! + ...
where A(x) = 1 + Series_Reversion( Integral 1/A(x)^3 dx ).
RELATED SERIES.
Integral 1/A(x)^3 dx = x - 3*x^2/2! + 3*x^3/3! - 24*x^4/4! - 261*x^5/5! - 6543*x^6/6! - 202671*x^7/7! - 7911351*x^8/8! + ...
where Integral 1/A(x)^3 dx = Series_Reversion(A(x) - 1).
A(A(x) - 1) = 1 + x + 6*x^2/2! + 75*x^3/3! + 1479*x^4/4! + 40617*x^5/5! + 1447785*x^6/6! + 64027656*x^7/7! + 3404869020*x^8/8! + ...
A(A(x) - 1)^3 = 1 + 3*x + 24*x^2/2! + 339*x^3/3! + 7101*x^4/4! + ...
where A(A(x) - 1)^3 = d/dx A(x).
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{a(n) = my(A=1+x+x*O(x^n)); for(i=0,n, A = 1 + serreverse(intformal(1/A^3))); n!*polcoeff(A,n)}
for(n=0,20,print1(a(n),", "))
Showing 1-2 of 2 results.