A159320 G.f.: A(x) = exp( Sum_{n>=1} (1 + C(2n-1,n-1)*x)^n * x^n/n ).

1, 1, 2, 5, 20, 158, 2474, 77743, 4991796, 594667388, 146257399827, 66417454104711, 61463521228604767, 107733377143686790760, 375280556077116698219547, 2553688433304747933172133639

Offset

0,3

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 + 158*x^5 + 2474*x^6 +...
log(A(x)) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+10*x)^3*x^3/3 + (1+35*x)^4*x^4/4 +...
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 59*x^4/4 + 676*x^5/5 + 13782*x^6/6 +...

Prog

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

Crossrefs

Cf. A159321 (log), A001700, A158872 (variant).

Sequence in context: A136650 A229662 A111885 * A184730 A181076 A156871

Adjacent sequences: A159317 A159318 A159319 * A159321 A159322 A159323

Keyword

nonn

Author

Paul D. Hanna, Apr 15 2009

Status

approved