A218120 G.f.: A(x) = exp( Sum_{n>=1} A069865(n)/2*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.

1, 1, 17, 260, 7244, 214257, 7593707, 287419304, 11745920475, 503237634257, 22503750152879, 1039694201489294, 49401095274561608, 2402478324494963930, 119201977436336120482, 6017223412990713126034, 308361587173800754305214, 16013543997544827365960598

Offset

0,3

Comments

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

exp( Sum_{n>=1} A000984(n)/2*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.

Links

Table of n, a(n) for n=0..17.

Formula

Self-convolution equals A218119.

Example

 G.f.: A(x) = 1 + x + 17*x^2 + 260*x^3 + 7244*x^4 + 214257*x^5 + 7593707*x^6 +...
log(A(x)) = x + 33*x^2/2 + 730*x^3/3 + 27425*x^4/4 + 1015626*x^5/5 + 43437282*x^6/6 + 1924149396*x^7/7 +...+ A069865(n)/2*x^n/n +...

Prog

 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^6)/2*x^m/m)+x*O(x^n)), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A218119, A166991, A166993, A218118, A069865.

Sequence in context: A048446 A001282 A135214 * A259849 A090380 A142898

Adjacent sequences: A218117 A218118 A218119 * A218121 A218122 A218123

Keyword

nonn

Author

Paul D. Hanna, Oct 21 2012

Status

approved