Well it's me, Marko Riedel. ;-)

Egorychev method for combinatorial number sums PDF and Riemann Zeta Function FEQ PDF and Coupon collector and EGFs PDF and Exponential formula PDF.

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Recommended reading:

• I. Mellin Transform Computation

• II. A sum formula by Hardy and Ramanujan

• III. Power Group Enumeration of $k$-subsets of a standard deck of 52 cards under suit permutation

• IV. Asymptotics of $\sum_{k=1}^n \sqrt[4]{k}$

• V. Burnside's lemma on non-isomorphic binary structures

• VI. Extreme Mellin transform computation

• VII. Branches of the logarithm

• VIII. Master Theorem Type computation

• IX. Additional Master Theorem Type computation

• X. More Master Theorem computations

• XI. Permutations of order k

• XII. Enumerating non-isomorphic graphs

• XIII. Fixed points in permutations raised to a power k

• XIV. A remarkable Mellin transform calculation

• XV. The trick with the $\pi\cot(\pi z)$ multiplier

• XVI. Barnes integral, Stirling numbers and coefficient asymptotics

• XVII. Enumerating labelled connected graphs

• XVIII. Plouffe, Apery and Mellin

• XIX. Double Stirling Number Identity

• XX. Another divergent Mellin transform

• XXI. Tree enumeration by LIF A (Lagrange Inversion Formula)

• XXII. Tree enumeration by LIF B

• XXIII. Tree enumeration by LIF C, two variables

• XXIV. Extreme binomial coefficients, residues

• XXV. More extreme binomial coefficients

• XXVI. Annihilating coefficient extractors and Stirling numbers

• XXVII. Trivariate permutation generating function

• XXVIII. Divergent series magic.

• XXVIX. EGFs for Stirling numbers

• XXX. Extreme binomial coefficients and roots of unity

• XXXI. Counting labelled / unlabelled endofunctions up to isomorphism

Recent work generally better than early work. Best-of.