A228648 G.f.: exp( Sum_{n>=1} A001609(n^2)*x^n/n ), where the l.g.f. of A001609 is -log(1-x-x^3).

1, 1, 3, 13, 128, 2974, 161048, 19632276, 5284440413, 3112165670205, 3990553641147871, 11107142249379896577, 66971338268043285905138, 873496931276771661395863398, 24617613776054408956962658439353, 1497874647146694311608664496205734267, 196633628592570082430451891781759097556806

Offset

0,3

Comments

A001609 forms the logarithmic derivative of Narayana's cows sequence A000930.

Links

Table of n, a(n) for n=0..16.

Formula

Logarithmic derivative yields A228647.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 13*x^3 + 128*x^4 + 2974*x^5 + 161048*x^6 +...
where
log(A(x)) = x + 5*x^2/2 + 31*x^3/3 + 453*x^4/4 + 14131*x^5/5 + 946781*x^6/6 + 136250983*x^7/7 +...+ A001609(n^2)*x^n/n +...

Prog

(PARI) {A001609(n)=n*polcoeff(-log(1-x-x^3 +x*O(x^n)), n)}
{a(n)=polcoeff(exp(sum(m=1, n+1, A001609(m^2)*x^m/m)+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A228647, A001609, A000930.

Sequence in context: A302861 A182864 A208590 * A161677 A180276 A054933

Adjacent sequences: A228645 A228646 A228647 * A228649 A228650 A228651

Keyword

nonn

Author

Paul D. Hanna, Aug 28 2013

Status

approved