A085023 E.g.f. satisfies exp(x*sum(n>=0, floor(a(n)/n!)*x^n)) = sum(n>=0, a(n)*x^n/n!).

1, 1, 3, 13, 97, 981, 12331, 187153, 3319233, 67362697, 1540796851, 39256807701, 1102344130273, 33822265578973, 1125785761963227, 40407886961046361, 1555858721974047361, 63972335301256871313, 2797676940942967706083

Offset

0,3

Comments

Floor(a(n)/n!) = A085022(n).

Links

Table of n, a(n) for n=0..18.

Example

exp(x*(1 + x + floor(3/2!)*x^2 + floor(13/3!)*x^3 + floor(97/4!)*x^4 + ...)) = 1 + x + (3/2!)*x^2 + (13/3!)*x^3 + (97/4!)*x^4 + ...

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=1+O(x); for(m=1, n, A=Pol(A)+x^m*(floor(polcoeff(exp(x*A), m))+O(x)); ); n!*polcoeff(exp(x*A), n))}

Crossrefs

Cf. A085022, A085295.

Sequence in context: A293528 A228160 A371319 * A144276 A083770 A084725

Adjacent sequences: A085020 A085021 A085022 * A085024 A085025 A085026

Keyword

nonn

Author

Paul D. Hanna, Jun 18 2003

Extensions

Example added by Vaclav Kotesovec, Apr 27 2015

Status

approved