A156306 E.g.f.: A(x) = exp( Sum_{n>=1} sigma(n) * a(n-1)*x^n/n! ) = Sum_{n>=0} a(n)*x^n/n! with a(0)=1.

1, 1, 4, 26, 292, 3468, 69664, 1208936, 32822456, 858979216, 28933584112, 836115182512, 40673697842208, 1381857061152896, 67261437417875776, 3297904559465926208, 192628214559932492928, 8815748379077085483264

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=1..n} sigma(k) * C(n-1,k-1)*a(k-1)*a(n-k) for n>0, with a(0)=1.

Example

E.g.f: A(x) = 1 + x + 4*x^2/2! + 26*x^3/3! + 292*x^4/4! + 3468*x^5/5! +...
log(A(x)) = x + 3*1*x^2/2! + 4*4*x^3/3! + 7*26*x^4/4! + 6*292*x^5/5! + 12*3468*x^6/6! +...

Prog

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

Crossrefs

Cf. A000203 (sigma).

Sequence in context: A177451 A304864 A167811 * A054592 A357795 A102202

Adjacent sequences: A156303 A156304 A156305 * A156307 A156308 A156309

Keyword

nonn

Author

Paul D. Hanna, Feb 08 2009

Status

approved