Una possibile soluzione
SELECT nextval nextval1, nextval nextval2
FROM
(
SELECT NEXTVAL('seq_name') nextval
) q
Ecco SQLFiddle demo.
AGGIORNAMENTO Per inserire al posto di INSERT INTO ... VALUES
usa INSERT INTO ... SELECT
INSERT INTO Table1 (col1, col2, col3, col4, ...)
SELECT nextval, nextval, 5, 'Text value', ...
FROM
(
SELECT NEXTVAL('seq_name') nextval
) q