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A188203 G.f.: exp( Sum_{n>=1} A188202(n)*x^n/n ) where A188202(n) = [x^n] (1 + 2^n*x + x^2)^n. 1
1, 2, 11, 206, 17586, 6878604, 11551087875, 80650796495414, 2307974943300931286, 268728588584911887188180, 126776477973814964972206209838, 241684409250478693507166916367088620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Compare to the g.f. M(x) of the Motzkin numbers (A001006):

M(x) = exp( Sum_{n>=1} A002426(n)*x^n/n) where A002426(n) = [x^n] (1+x+x^2)^n.

LINKS

Table of n, a(n) for n=0..11.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 11*x^2 + 206*x^3 + 17586*x^4 + 6878604*x^5 +...

The l.g.f. of A188202 begins:

log(A(x)) = 2*x + 18*x^2/2 + 560*x^3/3 + 68614*x^4/4 + 34210752*x^5/5 +...

The coefficients of x^n in (1 + 2^n*x + x^2)^n begin:

n=1: [1, (2), 1];

n=2: [1, 8, (18), 8, 1];

n=3: [1, 24, 195, (560), 195, 24, 1];

n=4: [1, 64, 1540, 16576, (68614), 16576, 1540, 64, 1];

n=5: [1, 160, 10245, 328320, 5273610, (34210752), 5273610, ...]; ...

where the central coefficients form the logarithmic derivative, A188202.

PROG

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, polcoeff((1+2^k*x+x^2+x*O(x^k))^k, k)*x^k/k)+x*O(x^n)), n)}

CROSSREFS

Cf. A188202 (log); variant: A001006.

Sequence in context: A226052 A271429 A051663 * A070256 A020450 A036229

Adjacent sequences:  A188200 A188201 A188202 * A188204 A188205 A188206

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 24 2011

STATUS

approved

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Last modified June 4 02:04 EDT 2020. Contains 334812 sequences. (Running on oeis4.)