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 A109955 Number triangle binomial(n+2k,3k). 4
 1, 1, 1, 1, 4, 1, 1, 10, 7, 1, 1, 20, 28, 10, 1, 1, 35, 84, 55, 13, 1, 1, 56, 210, 220, 91, 16, 1, 1, 84, 462, 715, 455, 136, 19, 1, 1, 120, 924, 2002, 1820, 816, 190, 22, 1, 1, 165, 1716, 5005, 6188, 3876, 1330, 253, 25, 1, 1, 220, 3003, 11440, 18564, 15504, 7315, 2024 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Riordan array (1/(1-x),x/(1-x)^3). Inverse array is A109956. Row sums are A052544. Diagonal sums are A034943(n+1). LINKS FORMULA Number triangle T(n, k) = binomial(n+2k, 3k). T(n,k) = 3*T(n-1,k) - 3*T(n-2,k) + T(n-3,k) + T(n-1,k-1). - Philippe Deléham, Feb 18 2012 G.f.: (1-x)^2/((1-x)^3-y*x). - Philippe Deléham, Feb 18 2012 Sum_{k, 0<=k<=n} T(n,k)*x^k = A185963(n), A000012(n), A052544(n), A049086(n) for x = -1, 0, 1, 2 respectively. - Philippe Deléham, Feb 18 2012 EXAMPLE Rows begin 1; 1,1; 1,4,1; 1,10,7,1; 1,20,28,10,1; 1,35,84,55,13,1; PROG (PARI) tabl(nn) = {my(m = matrix(nn, nn, n, k, if (n

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)