A181076 G.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^n *x^k ] *x^n/n ).

1, 1, 2, 5, 20, 168, 3659, 204644, 25503314, 7434144333, 5248999682258, 8079852389207554, 28328874782544308254, 244277149833867010587231, 4673118265932181394325207044, 198007423467261943865049734612821

Offset

0,3

Comments

Conjecture: this sequence consists entirely of integers.

Links

Table of n, a(n) for n=0..15.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 20*x^4 + 168*x^5 + 3659*x^6 +...
The logarithm begins:
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 59*x^4/4 + 726*x^5/5 + 20832*x^6/6 +...+ A181077(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 + 2^2*x + 3^2*x^2 + 4^2*x^3 + 5^2*x^4 + 6^2*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 + 4^4*x + 10^4*x^2 + 20^4*x^3 + 35^4*x^4 + 56^4*x^5 +...)*x^4/4
+ (1 + 5^5*x + 15^5*x^2 + 35^5*x^3 + 70^5*x^4 + 126^5*x^5 +...)*x^5/5
+ (1 + 6^6*x + 21^6*x^2 + 56^6*x^3 + 126^6*x^4 + 252^6*x^5 +...)*x^6/6
+ (1 + 7^7*x + 28^7*x^2 + 84^7*x^3 + 210^7*x^4 + 462^7*x^5 +...)*x^7/7 +...

Prog

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

Crossrefs

Cf. A181077 (log), variants: A181074, A181078.

Sequence in context: A111885 A159320 A184730 * A156871 A058109 A005331

Adjacent sequences: A181073 A181074 A181075 * A181077 A181078 A181079

Keyword

nonn

Author

Paul D. Hanna, Oct 02 2010

Status

approved