A300047 E.g.f. L(x) satisfies: L(x) = log(1 + Integral exp( L(4*x)/2 ) dx).

1, 1, 8, 270, 35472, 18318288, 37611139104, 308338698386160, 10105807430398162176, 1324669305373789482964224, 694520145536868530329362481152, 1456521257891915020152240334073326080, 12218201898131114878545053215635303915614208, 409974971372215896118360380056730403849666983370752

Offset

1,3

Links

Table of n, a(n) for n=1..14.

Formula

E.g.f.: L(x) = log(G(x)) where G(x) is the e.g.f. of A300045.

Example

E.g.f.: L(x) = x + x^2/2! + 8*x^3/3! + 270*x^4/4! + 35472*x^5/5! + 18318288*x^6/6! + 37611139104*x^7/7! + 308338698386160*x^8/8! + 10105807430398162176*x^9/9! + ...
Related series.
exp(L(x)) = 1 + x + 2*x^2/2! + 12*x^3/3! + 312*x^4/4! + 37008*x^5/5! + 18540576*x^6/6! + ... + A300045(n)*x^n/n! + ...
exp(L(4*x)/2) = 1 + 2*x + 12*x^2/2! + 312*x^3/3! + 37008*x^4/4! + 18540576*x^5/5! + ... + A300045(n+1)*x^n/n! + ...
exp(L(2*x)/2) = 1 + x + 3*x^2/2! + 39*x^3/3! + 2313*x^4/4! + 579393*x^5/5! + 589702779*x^6/6! + ... + A300046(n)*x^n/n! + ...

Prog

(PARI) {a(n) = my(A=1+x); for(i=1, n, A = 1 + intformal(subst(A, x, 4*x)^(1/2) +x*O(x^n) )); n!*polcoeff(log(A), n)}
for(n=1, 16, print1(a(n), ", "))

Crossrefs

Cf. A300045, A300046.

Sequence in context: A326920 A221606 A230590 * A336214 A129424 A274559

Adjacent sequences: A300044 A300045 A300046 * A300048 A300049 A300050

Keyword

nonn

Author

Paul D. Hanna, Feb 25 2018

Status

approved