A380842 Main diagonal of the array A380841.

1, 1, 10, 141, 2776, 70045, 2157156, 78452521, 3290644288, 156380715801, 8304267312100, 487328231729581, 31318669850761008, 2187567259278425557, 165011952533314548676, 13368463736048341225425, 1157693100510102752463616, 106719312722496774534400177, 10433609651067618426072766020

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(k+n-1,k)/(n-k)!. - Seiichi Manyama, Feb 06 2025

Mathematica

A380841[n_, k_]:=n!SeriesCoefficient[1/(1-x*Exp[x])^k, {x, 0, n}]; Table[A380841[n, n], {n, 0, 18}]

Prog

(PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(k+n-1, k)/(n-k)!); \\ Seiichi Manyama, Feb 06 2025

Crossrefs

Cf. A213643, A380841.

Sequence in context: A277310 A343689 A277372 * A181162 A245988 A184710

Adjacent sequences: A380837 A380838 A380841 * A380843 A380844 A380845

Keyword

nonn,new

Author

Stefano Spezia, Feb 05 2025

Status

approved