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A181066 G.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^3 *x^k ] *x^n/n ). 2
1, 1, 2, 7, 31, 157, 865, 5051, 30774, 193669, 1250319, 8240232, 55239187, 375624781, 2585449450, 17982937876, 126222946496, 893073250063, 6363674671524, 45631735776036, 329065051395940, 2385126419825231 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare g.f. to a g.f. of the Catalan numbers (A000108):

. exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^2 *x^k ] *x^n/n ).

LINKS

Table of n, a(n) for n=0..21.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 31*x^4 + 157*x^5 + 865*x^6 +...

The logarithm begins:

log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 95*x^4/4 + 606*x^5/5 + 4032*x^6/6 +...+ A181067(n)*x^n/n +...

which equals the series:

log(A(x)) = (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 +...)*x

+ (1 + 2^3*x + 3^3*x^2 + 4^3*x^3 + 5^3*x^4 + 6^3*x^5 +...)*x^2/2

+ (1 + 3^3*x + 6^3*x^2 + 10^3*x^3 + 15^3*x^4 + 21^3*x^5 +...)*x^3/3

+ (1 + 4^3*x + 10^3*x^2 + 20^3*x^3 + 35^3*x^4 + 56^3*x^5 +...)*x^4/4

+ (1 + 5^3*x + 15^3*x^2 + 35^3*x^3 + 70^3*x^4 + 126^3*x^5 +...)*x^5/5

+ (1 + 6^3*x + 21^3*x^2 + 56^3*x^3 + 126^3*x^4 + 252^3*x^5 +...)*x^6/6

+ (1 + 7^3*x + 28^3*x^2 + 84^3*x^3 + 210^3*x^4 + 462^3*x^5 +...)*x^7/7 +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, n, binomial(m+k-1, k)^3*x^k)*x^m/m)+x*O(x^n)), n)}

CROSSREFS

Cf. A181067 (log), A181068 (variant).

Sequence in context: A030823 A030873 A030913 * A325452 A030945 A088554

Adjacent sequences:  A181063 A181064 A181065 * A181067 A181068 A181069

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 03 2010

STATUS

approved

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Last modified July 22 11:00 EDT 2019. Contains 325219 sequences. (Running on oeis4.)