cp's OEIS Frontend

A109955 Number triangle binomial(n+2k,3k).

%I A109955 #14 Nov 20 2015 05:25:42
%S A109955 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,
%T A109955 1,1,84,462,715,455,136,19,1,1,120,924,2002,1820,816,190,22,1,1,165,
%U A109955 1716,5005,6188,3876,1330,253,25,1,1,220,3003,11440,18564,15504,7315,2024
%N A109955 Number triangle binomial(n+2k,3k).
%C A109955 Riordan array (1/(1-x),x/(1-x)^3).
%C A109955 Inverse array is A109956. Row sums are A052544.
%C A109955 Diagonal sums are A034943(n+1).
%F A109955 Number triangle T(n, k) = binomial(n+2k, 3k).
%F A109955 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
%F A109955 G.f.: (1-x)^2/((1-x)^3-y*x). - _Philippe Deléham_, Feb 18 2012
%F A109955 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
%e A109955 Rows begin
%e A109955 1;
%e A109955 1,1;
%e A109955 1,4,1;
%e A109955 1,10,7,1;
%e A109955 1,20,28,10,1;
%e A109955 1,35,84,55,13,1;
%o A109955 (PARI) tabl(nn) = {my(m = matrix(nn, nn, n, k, if (n<k, 0, binomial(n+2*k-3, 3*k-3)))); for (n=1, nn, for (k=1, n, print1(m[n, k], ", ");); print(););} \\ _Michel Marcus_, Nov 20 2015
%K A109955 easy,nonn,tabl
%O A109955 0,5
%A A109955 _Paul Barry_, Jul 06 2005