A351527 -id:A351527 - cp's OEIS frontend

A351525 Expansion of e.g.f. (log(1 + log(1 + log(1+ x))))^2 / 2.

1, -9, 87, -975, 12657, -188090, 3159699, -59326371, 1232843529, -28116615263, 698649506871, -18796044698977, 544507930693022, -16903759793180115, 559960766050363931, -19719027513960290370, 735696883534117583082, -28991986984973263419262

Offset: 2

Seiichi Manyama, Feb 13 2022

sign

Column 2 of A039815.

Cf. A000268, A341587, A351513, A351526, A351527.

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));

a(n) = (-1)^n * Sum_{k=1..n-1} binomial(n-1,k) * A000268(k) * A000268(n-k).

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

Seiichi Manyama, Feb 13 2022

sign

Column 2 of A039816.

Cf. A000310, A341587, A351514, A351525, A351527.

my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+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, 4)*T(n-k, 4));

a(n) = (-1)^n * Sum_{k=1..n-1} binomial(n-1,k) * A000310(k) * A000310(n-k).

cp's OEIS Frontend

A351525 Expansion of e.g.f. (log(1 + log(1 + log(1+ x))))^2 / 2.

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A351526 Expansion of e.g.f. (log(1 + log(1 + log(1 + log(1+ x)))))^2 / 2.

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula