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Results tagged with integer-sequences
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user 10744
For questions about sequences of integers. References are often made to the online resource oeis.org.
32
votes
Accepted
Integrality of a sequence formed by sums
Let $A(x) = \sum_{n=1}^\infty a_n x^n$ and let
$$S(x) = \sum_{k=0}^\infty (7k+8)\frac{(3k+1)!}{k!\,(2k+3)!} x^k.$$
Then the formula for $a_n$ gives
$A(x) = R(x)S(x)$,
where
$$R(x) = \frac{1}{3}\biggl( …
- 17k
4
votes
Integrality of a sequence formed by sums
Here is another proof, inspired by Tewodros Amdeberhan's. We represent the sum as a constant term in a power series.
To represent $(7k+8) \frac{(3k+1)!}{k!\,(2k+3)!}$ as a constant term, we need to ex …
- 17k
6
votes
Accepted
Closed form for the A110501 (unsigned Genocchi numbers (of first kind) of even index)
This is a known result. To quote from Richard Stanley's Enumerative Combinatorics, Volume 2, second edition, solution to problem 8(e) of Chapter 5, page 115: This is equivalent to a conjecture of J. M …
- 17k