login
A368535
a(n) = Sum_{k=1..n} binomial(k+2,3) * n^(n-k).
1
0, 1, 6, 31, 188, 1510, 16106, 217938, 3577624, 68952495, 1524157870, 37974983321, 1052320304212, 32089921353308, 1067586804710258, 38470738234990580, 1492501011869912496, 62015249735222969325, 2747431806313734355830, 129267455591507496073315
OFFSET
0,3
FORMULA
a(n) = [x^n] x/((1-n*x) * (1-x)^4).
a(n) = n * (6*n^(n+2) - n^5 - 3*n^4 + n^3 + n^2 - 6*n + 2)/(6 * (n-1)^4) for n > 1.
PROG
(PARI) a(n) = sum(k=1, n, binomial(k+2, 3)*n^(n-k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 29 2023
STATUS
approved