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A181068 G.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^4 *x^k ] *x^n/n ). 2
1, 1, 2, 11, 80, 714, 7095, 76206, 864590, 10227727, 125001862, 1568419058, 20108619244, 262510020319, 3479914302802, 46742907726147, 635092339459857, 8716058291255777, 120686879727465365, 1684357785848110976 (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..19.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 11*x^3 + 80*x^4 + 714*x^5 + 7095*x^6 +...

The logarithm begins:

log(A(x)) = x + 3*x^2/2 + 28*x^3/3 + 275*x^4/4 + 3126*x^5/5 + 37632*x^6/6 +...+ A181069(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 + 2^4*x + 3^4*x^2 + 4^4*x^3 + 5^4*x^4 + 6^4*x^5 +...)*x^2/2

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

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

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

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

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

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, n, binomial(m+k-1, k)^4*x^k)*x^m/m)+x*O(x^n)), n)}

CROSSREFS

Cf. A181069 (log), A181066 (variant).

Sequence in context: A099661 A027110 A118969 * A056846 A277500 A197718

Adjacent sequences:  A181065 A181066 A181067 * A181069 A181070 A181071

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 08 2010

STATUS

approved

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)