We introduce a new exponential family F₃ as follows: first, for each n≥1, in the deck D_n there is just one card of weight n. On that card there is a picture of a smiling rabbit^*, and there is the label set [n].→[More:]


^*Why not? Since there's only one card the picture is immaterial, so it might as well be cheerful.

--H.S. Wilf, Generatingfunctionology.