A291903 Sums of the fourth powers of the descent set statistics for permutations on n elements.

1, 1, 2, 34, 1576, 190216, 46479536, 21246061600, 16505196258944, 20569621110703360, 39048520577674054912, 108556407221350072075840, 427386074980323385950161920, 2317659324414032887611600999424, 16904848426143946143993568391307264, 162490636486997482412425606460112242944, 2021898321663894965658036079204603050491904

Offset

0,3

Links

Table of n, a(n) for n=0..16.

R. Ehrenborg and A. Happ, On the powers of the descent set statistic, arXiv:1709.00778 [math.CO], 2017.

Formula

a(n) = Sum_{j=0..ceiling(2^(n-1))-1} A060351(n,j)^4. - Alois P. Heinz, Sep 15 2020

Example

For n=4, we have a(4) = 1^4 + 3^4 + 5^4 + 3^4 + 3^4 + 5^4 + 3^4 + 1^4 = 1576.

Crossrefs

Cf. A060350, A291902, A291907, A060351.

Column k=4 of A334622.

Sequence in context: A195005 A215957 A171732 * A340863 A198977 A198718

Adjacent sequences: A291900 A291901 A291902 * A291904 A291905 A291906

Keyword

nonn

Author

Richard Ehrenborg, Sep 05 2017

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 09 2020

Status

approved