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 A109971 Inverse of Riordan array (1,x(1-x)^2), A109970. 4
 1, 0, 1, 0, 2, 1, 0, 7, 4, 1, 0, 30, 18, 6, 1, 0, 143, 88, 33, 8, 1, 0, 728, 455, 182, 52, 10, 1, 0, 3876, 2448, 1020, 320, 75, 12, 1, 0, 21318, 13566, 5814, 1938, 510, 102, 14, 1, 0, 120175, 76912, 33649, 11704, 3325, 760, 133, 16, 1, 0, 690690, 444015, 197340 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are A001764. Diagonal sums are A109972. Second column is A006013. Third column is A006629. LINKS Naiomi Cameron, J. E. McLeod, Returns and Hills on Generalized Dyck Paths, Journal of Integer Sequences, Vol. 19, 2016, #16.6.1. W.-j. Woan, The Lagrange inversion formula and divisibility properties, JIS 10 (2007) 07.7.8, example 4. FORMULA Number triangle T(0, 0)=1, T(0, k)=0, k>0, T(n, k)=(k/n)*binomial(3n-k-1, n-k) otherwise; Riordan array (1, f) where f(1-f)^2=x. T(n, k)=sum{j=0..n, ((3j+1)/(2n+j+1))(-1)^(j-k)*C(3n, 2n+j)C(j, k)}; - Paul Barry, Oct 07 2005 T(n,k)=binomial(3n-k,n-k)*2k/(3n-k). (Paul Barry, May 18 2006) EXAMPLE Rows begin 1; 0,1; 0,2,1; 0,7,4,1; 0,30,18,6,1; 0,143,88,33,8,1; Production array begins 0, 1 0, 2, 1 0, 3, 2, 1 0, 4, 3, 2, 1 0, 5, 4, 3, 2, 1 0, 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1 0, 8, 7, 6, 5, 4, 3, 2, 1 0, 9, 8, 7, 6, 5, 4, 3, 2, 1 ... - Philippe Deléham, Mar 05 2013 CROSSREFS Essentially the same as A092276. Sequence in context: A174869 A330862 A269158 * A284797 A316135 A327620 Adjacent sequences:  A109968 A109969 A109970 * A109972 A109973 A109974 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Jul 06 2005 STATUS approved

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Last modified June 21 06:24 EDT 2021. Contains 345358 sequences. (Running on oeis4.)