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Search: id:A115351
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| A115351 |
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Sum of interior Multinomial Coefficient components. |
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+0
1
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| 1, 1, 0, 0, 11, 96, 798, 6197, 54400, 505503, 5241223, 58377002, 712436696, 9315437345, 131487856629, 1978064399766, 31777977184459, 541010185315536, 9758067888585784, 185538235462354828, 3714549428287398782
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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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.
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FORMULA
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a(n) = A005651(n) - A000142(n) - A000085(n) - A000041(n) + 3
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EXAMPLE
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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
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CROSSREFS
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Cf. A000041, A000085, A000142, A005651, A097522, A104778.
Sequence in context: A016203 A055286 A081041 this_sequence A137017 A133833 A142260
Adjacent sequences: A115348 A115349 A115350 this_sequence A115352 A115353 A115354
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KEYWORD
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nonn
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Jan 20 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2008
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