A115351 Sum of interior Multinomial Coefficient components.

1, 1, 0, 0, 11, 96, 798, 6197, 54400, 505503, 5241223, 58377002, 712436696, 9315437345, 131487856629, 1978064399766, 31777977184459, 541010185315536, 9758067888585784, 185538235462354828, 3714549428287398782

Offset

0,5

Comments

For a given value of n, the multinomial coefficients can be decomposed into components arranged in triangular fashion, as illustrated in A097522 and A104707. The values on the three edges sum to A000142(n), A000085(n) and A000041(n) respectively. Since each vertex component has the value one and appears on two of the three edges the formula is adjusted by three.

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = A005651(n) - A000142(n) - A000085(n) - A000041(n) + 3

Example

a(5) = 96 because the sum for the below triangle is 246 and the three edges sum to 120, 26 and 7; therefore 246 - (120 + 26 + 7 - 3) = 96.
1
16 1
25 12 1
36 15 8 1
25 18 10 8 1
16 10 6 5 4 1
1 4 5 6 5 4 1

Crossrefs

Cf. A000041, A000085, A000142, A005651, A097522, A104778.

Sequence in context: A055286 A081041 A294724 * A154997 A137017 A133833

Adjacent sequences: A115348 A115349 A115350 * A115352 A115353 A115354

Keyword

nonn

Author

Alford Arnold, Jan 20 2006

Extensions

More terms from R. J. Mathar, Jan 23 2008

Status

approved