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

2,2

Links

Table of n, a(n) for n=2..19.

Formula

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

Mathematica

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 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+log(1+log(1+x)))^2/2))
(PARI) 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));

Crossrefs

Column 2 of A039815.

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

Sequence in context: A267265 A152264 A035101 * A245491 A160466 A362509

Adjacent sequences: A351522 A351523 A351524 * A351526 A351527 A351528

Keyword

sign

Author

Seiichi Manyama, Feb 13 2022

Status

approved