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A109972 Diagonal sums of number triangle A109970. 1
1, 0, 1, 2, 8, 34, 162, 822, 4365, 23956, 134814, 773746, 4511693, 26652346, 159170385, 959412290, 5829083420, 35661048886, 219491344362, 1358204062536, 8444658457530, 52729475008690, 330518562341537, 2078987880103170 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..23.

Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.

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]

PROG

(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

CROSSREFS

Sequence in context: A150901 A046649 A174808 * A019023 A030857 A030894

Adjacent sequences:  A109969 A109970 A109971 * A109973 A109974 A109975

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 06 2005

STATUS

approved

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Last modified September 17 17:25 EDT 2019. Contains 327136 sequences. (Running on oeis4.)