A369723
Expansion of e.g.f. exp( 2 * (1-sqrt(1-4*x)) ).
Original entry on oeis.org
1, 4, 24, 208, 2464, 37824, 720256, 16450816, 439245312, 13440572416, 464007387136, 17847329869824, 757011972726784, 35108108023349248, 1767517592731090944, 96007679735852498944, 5596725706163142393856, 348533116657888468402176
Offset: 0
A369724
Expansion of e.g.f. exp( (5/2) * (1-sqrt(1-4*x)) ).
Original entry on oeis.org
1, 5, 35, 335, 4225, 67525, 1321075, 30751775, 832573025, 25745985125, 896177819875, 34698406783375, 1479737530398625, 68935386567921125, 3483762766656021875, 189846574063623209375, 11098195364856546690625, 692834276972696475053125
Offset: 0
A369746
Expansion of e.g.f. exp( 3 * (1-sqrt(1-2*x)) ).
Original entry on oeis.org
1, 3, 12, 63, 423, 3528, 35559, 422901, 5817744, 91072269, 1600588269, 31230827532, 670252672593, 15696888917427, 398454496989012, 10899543418960167, 319672849622745951, 10007954229075765984, 333139545206104991031, 11749955670275356579941
Offset: 0
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# The row polynomials of A132062 evaluated at x = 3.
T := proc(n, k) option remember; if k = 0 then 0^n elif n < k then 0
else (2*(n - 1) - k)*T(n - 1, k) + T(n - 1, k - 1) fi end:
seq(add(T(n, k)*3^k, k = 0..n), n = 0..19); # Peter Luschny, Apr 25 2024
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With[{nn=20},CoefficientList[Series[Exp[3(1-Sqrt[1-2x])],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Apr 14 2025 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*(1-sqrt(1-2*x)))))
Showing 1-3 of 3 results.