A109972 Diagonal sums of number triangle A109970.
1, 0, 1, 2, 8, 34, 162, 822, 4365, 23956, 134814, 773746, 4511693, 26652346, 159170385, 959412290, 5829083420, 35661048886, 219491344362, 1358204062536, 8444658457530, 52729475008690, 330518562341537, 2078987880103170
Offset: 0
Links
- Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.
Programs
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PARI
a(n) = if (n==0, 1, sum(k=0, n-1, (k/(n-k))*binomial(3*n-4*k-1, n-2*k))); \\ Michel Marcus, Jan 25 2019
Formula
a(0) = 1, a(n) = Sum_{k=0..n-1} (k/(n-k))*binomial(3n-4k-1, n-2k), n>0. [corrected by Michel Marcus, Jan 25 2019]