A351513
Expansion of e.g.f. (exp(exp(exp(x)-1)-1)-1)^2 / 2.
Original entry on oeis.org
1, 9, 75, 660, 6288, 65051, 728556, 8792910, 113805204, 1572387410, 23094192960, 359209182397, 5896792771795, 101854538628396, 1846058978130172, 35021271971160507, 693843099578350329, 14326635965967487711, 307729547549467823822, 6864250658908517748384
Offset: 2
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my(N=40, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(x)-1)-1)-1)^2/2))
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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, 3)*T(n-k, 3));
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
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my(N=20, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)^2/2))
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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));
A351526
Expansion of e.g.f. (log(1 + log(1 + log(1 + log(1+ x)))))^2 / 2.
Original entry on oeis.org
1, -12, 152, -2210, 36976, -704837, 15132932, -362099010, 9566898126, -276863733707, 8715530417502, -296641340905299, 10858928017129838, -425542158316462627, 17779220784851800828, -789053832262002586555, 37076561046965367191298
Offset: 2
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my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+log(1+log(1+log(1+x))))^2/2))
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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, 4)*T(n-k, 4));
Showing 1-3 of 3 results.