A085022 Integer floor of coefficients of exp(x*A(x)).

1, 1, 1, 2, 4, 8, 17, 37, 82, 185, 424, 983, 2301, 5431, 12913, 30900, 74361, 179855, 436974, 1065985, 2609993, 6411730, 15799090, 39039031, 96711591, 240150955, 597640140, 1490309462, 3723343793, 9318686066, 23360994967, 58654055246

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..350

Formula

a(n) = floor(A085023(n)/n!) where exp(x*A(x)) = sum(n>=0, A085023(n)*x^n/n!).

a(n) ~ c * d^n / n^(3/2), where d = 2.6325509689919889304486..., c = 0.99440959889640775375... . - Vaclav Kotesovec, Apr 27 2015

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 + ...
1 + x + floor(3/2)*x^2 + floor(13/6)*x^3 + floor(97/24)*x^4 + ... = 1 + x + x^2 + 2*x^3 + 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)); ); polcoeff(A, n))}

Crossrefs

Cf. A085023, A085294.

Sequence in context: A203019 A004148 A292460 * A324936 A358453 A331783

Adjacent sequences: A085019 A085020 A085021 * A085023 A085024 A085025

Keyword

nonn

Author

Paul D. Hanna, Jun 18 2003

Extensions

Example added by Vaclav Kotesovec, Apr 27 2015

Status

approved