Original entry on oeis.org
1, -1, 1, 2, -3, 1, -7, 12, -6, 1, 37, -67, 39, -10, 1, -266, 495, -310, 95, -15, 1, 2431, -4596, 3000, -1010, 195, -21, 1, -27007, 51583, -34566, 12320, -2660, 357, -28, 1, 353522, -680037, 463981, -171766, 39795, -6062, 602, -36, 1, -5329837, 10306152, -7124454, 2709525, -658791, 108927, -12432, 954
Offset: 0
Triangle begins:
1;
-1,1;
2,-3,1;
-7,12,-6,1;
37,-67,39,-10,1;
-266,495,-310,95,-15,1;
2431,-4596,3000,-1010,195,-21,1;
-27007,51583,-34566,12320,-2660,357,-28,1; ...
and is the matrix inverse of A100862:
1;
1,1;
1,3,1;
1,6,6,1;
1,10,21,10,1;
1,15,55,55,15,1; ...
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{T(n,k)=local(X=x+x*O(x^n),Y=y+y*O(y^n));(matrix(n+1,n+1,m,j,if(m>=j, (m-1)!*polcoeff(polcoeff(exp(X+Y*X^2/2+X*Y),m-1,x),j-1,y)))^-1)[n+1,k+1]}
A107103
Column 1 of triangle A107102, which is the matrix inverse of A100862.
Original entry on oeis.org
1, -3, 12, -67, 495, -4596, 51583, -680037, 10306152, -176591665, 3376207461, -71258869848, 1645797382177, -41289185878227, 1118136109703460, -32509366699961371, 1010047705084550823, -33397162601828122332, 1170937325957822375167, -43391988679237460897205
Offset: 0
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{a(n)=local(X=x+x^2*O(x^n),Y=y+y^2*O(y^n));(matrix(n+2,n+2,m,k,if(m>=k, (m-1)!*polcoeff(polcoeff(exp(X+Y*X^2/2+X*Y),m-1,x),k-1,y)))^-1)[n+2,2]}
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.
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