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

Author

Alford Arnold, Jan 20 2006

Keywords

• nonn

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.

Examples

			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.

Formula

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

Extensions

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