A368535 a(n) = Sum_{k=1..n} binomial(k+2,3) * n^(n-k).

0, 1, 6, 31, 188, 1510, 16106, 217938, 3577624, 68952495, 1524157870, 37974983321, 1052320304212, 32089921353308, 1067586804710258, 38470738234990580, 1492501011869912496, 62015249735222969325, 2747431806313734355830, 129267455591507496073315

Offset

0,3

Links

Table of n, a(n) for n=0..19.

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

Cf. A062805, A368534.

Cf. A002663, A097786, A097788.

Sequence in context: A199320 A097176 A361306 * A362387 A121754 A351818

Adjacent sequences: A368532 A368533 A368534 * A368536 A368537 A368538

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 29 2023

Status

approved