A351514
Expansion of e.g.f. (exp(exp(exp(exp(x)-1)-1)-1)-1)^2 / 2.
Original entry on oeis.org
1, 12, 136, 1650, 21904, 318521, 5051988, 86910426, 1612648066, 32107793135, 682724688430, 15439016490989, 369914992674530, 9359103270641290, 249292192469843244, 6971850327184526783, 204215496402215939638, 6251233458455082035922
Offset: 2
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(exp(x)-1)-1)-1)-1)^2/2))
-
T(n, k) = if(k==0, n<=1, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
a(n) = sum(k=1, n-1, binomial(n-1, k)*T(k, 4)*T(n-k, 4));
A351515
Expansion of e.g.f. (exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)^2 / 2.
Original entry on oeis.org
1, 15, 215, 3325, 56605, 1060780, 21772595, 486459105, 11760431325, 305942552245, 8521928511915, 253041654671949, 7977871631560394, 266128899746035160, 9363456107172891499, 346487270686107589124, 13450341325170239245308, 546470289216642540029570
Offset: 2
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)^2/2))
-
T(n, k) = if(k==0, n<=1, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
a(n) = sum(k=1, n-1, binomial(n-1, k)*T(k, 5)*T(n-k, 5));
A351525
Expansion of e.g.f. (log(1 + log(1 + log(1+ x))))^2 / 2.
Original entry on oeis.org
1, -9, 87, -975, 12657, -188090, 3159699, -59326371, 1232843529, -28116615263, 698649506871, -18796044698977, 544507930693022, -16903759793180115, 559960766050363931, -19719027513960290370, 735696883534117583082, -28991986984973263419262
Offset: 2
-
With[{nn=20},CoefficientList[Series[Log[1+Log[1+Log[1+x]]]^2/2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 15 2024 *)
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+log(1+log(1+x)))^2/2))
-
T(n, k) = if(k==0, n==1, sum(j=0, n, abs(stirling(n, j, 1))*T(j, k-1)));
a(n) = (-1)^n*sum(k=1, n-1, binomial(n-1, k)*T(k, 3)*T(n-k, 3));
Showing 1-3 of 3 results.