A395476 Expansion of e.g.f. x^3*(1 + x + x^2/2)*exp(x).

0, 0, 0, 6, 48, 240, 840, 2310, 5376, 11088, 20880, 36630, 60720, 96096, 146328, 215670, 309120, 432480, 592416, 796518, 1053360, 1372560, 1764840, 2242086, 2817408, 3505200, 4321200, 5282550, 6407856, 7717248, 9232440, 10976790, 12975360, 15254976, 17844288, 20773830

Offset

0,4

Comments

Number of words of length n defined on {a, b, c, d, e} that contain one a, one b, one c, at most two d's, and any number of e's.

Links

Table of n, a(n) for n=0..35.

Formula

a(n) = n*(n-1)*(n-2)*(n^2-5*n+8)/2.

a(n) = 6*binomial(n,3)*Sum_{k=0..2} binomial(n-3,k).

Crossrefs

Cf. A047927.

Sequence in context: A260344 A353247 A262354 * A395461 A052771 A056289

Adjacent sequences: A395473 A395474 A395475 * A395477 A395478 A395479

Keyword

nonn,easy

Author

Enrique Navarrete, Apr 24 2026

Status

approved