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сладко стянул
сначала вспомним, как перемножаются экспоненциальные производящие функции: почти так же, как обычные (происходит свёртка), но при свёртке — биномиальный коэффициент. У нас B(t)=exp(t) или exp(-t), то есть b_l = 1 или b_l = (-1)^l
Домножим G(t) на exp(-t). Оказывается, наш многочлен имеет "целые" коэффициенты.

Домножим обратно на exp(t). Получается формула для g_k при k>>0, в которой параметр k встречается только в биномиальном коэффициенте. Всё остальное "фиксированное" и "целочисленное".



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Домножим G(t) на exp(-t). Оказывается, наш многочлен имеет "целые" коэффициенты.

Домножим обратно на exp(t). Получается формула для g_k при k>>0, в которой параметр k встречается только в биномиальном коэффициенте. Всё остальное "фиксированное" и "целочисленное".

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