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Search: id:A102639
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| A102639 |
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Combinatorial triangle !n. This table read by rows gives the coefficients of general sum formulae of n-th Left factorials (A003422). The k-th row (k>=1) contains T(i,k) for i=1 to 2*k and k=1 to n-2, where T(i,k) satisfies !n = n + Sum_{k=1..n-2} Sum_{i=1..2*k} T(i,k) * C(n-k-1,i). |
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| 1, 1, 3, 8, 8, 3, 9, 46, 101, 114, 65, 15, 33, 272, 975, 1935, 2289, 1615, 630, 105, 153, 1796, 9175, 26795, 49474, 60080, 48104, 24535, 7245, 945, 873, 13424, 90255, 353507, 902164, 1582455, 1953272, 1700860, 1025927, 408870, 97020, 10395, 5913
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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The coefficients T(i,k) along the i-th columns of the triangle are the consecutive partial sums of those found in table A094216.
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LINKS
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A. F. Labossiere, Sobalian Coefficients.
A. F. Labossiere, Miscellaneous.
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EXAMPLE
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!7 = 7 + 1*C(7-2,1) + 1*C(7-2,2) + 3*C(7-3,1) + ... + 33*C(7-5,1) + 272*C(7-5,2) + 153*C(7-6,1) = 7 + 5 + 10 + 12 + 8*C(4,2) + 8*C(4,3) + 3*C(4,4) + 9*C(3,1) + 46*C(3,2) + 101*C(3,3) + 66 + 272 + 153 = 7 + 5 + 10 + 12 + 48 + 32 + 3 + 27 + 138 + 101 + 66 + 272 + 153 = 874.
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CROSSREFS
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Cf. A094216, A102411, A102412, A101752, A003422, A094638, A008276.
Sequence in context: A019630 A101749 A019744 this_sequence A118817 A131596 A065481
Adjacent sequences: A102636 A102637 A102638 this_sequence A102640 A102641 A102642
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KEYWORD
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nonn,tabl
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AUTHOR
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Andre F. Labossiere (boronali(AT)laposte.net), Feb 01 2005
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