cp's OEIS Frontend

A338372 T(n, m) = Sum_{k=1..(m+3)/2} C(m-k+2, k-1)*C(n+1, k-1)*C(n-m+k-1, k-1)*C(2*n-2*k+4, 2*m-4*k+5)/(C(2*k-2, k-1)*C(2*m-2*k+4, 2*k-2))/2, triangle read by rows.

%I A338372 #10 Oct 23 2020 07:54:10
%S A338372 1,2,2,3,10,4,4,28,32,8,5,60,136,88,16,6,110,416,504,224,32,7,182,
%T A338372 1036,2024,1616,544,64,8,280,2240,6448,8064,4736,1280,128,9,408,4368,
%U A338372 17424,31456,28288,13056,2944,256,10,570,7872,41616,102592,130880,90880,34432,6656,512,11,770,13332,90288,291808,501568,487040,273792,87808,14848,1024
%N A338372 T(n, m) = Sum_{k=1..(m+3)/2} C(m-k+2, k-1)*C(n+1, k-1)*C(n-m+k-1, k-1)*C(2*n-2*k+4, 2*m-4*k+5)/(C(2*k-2, k-1)*C(2*m-2*k+4, 2*k-2))/2, triangle read by rows.
%F A338372 G.f.: -1/(x^2*y^2 - (1 - x*(y + 2*A001263(x, y) + 1))^2) = 1/(1 - 2*x^2*y + x^2 - 2*x*y - 2*x).
%e A338372 1,
%e A338372 2, 2,
%e A338372 3, 10, 4,
%e A338372 4, 28, 32, 8,
%e A338372 5, 60, 136, 88, 16
%p A338372 ogf := 1/(1 -2*x^2*y + x^2 - 2*x*y - 2*x): ser := series(ogf, x, 22):
%p A338372 xser := n -> expand(coeff(ser, x, n)):
%p A338372 seq(seq(coeff(xser(n), y, k), k=0..n), n=0..10); # _Peter Luschny_, Oct 23 2020
%o A338372 (Maxima)
%o A338372 T(n,m):=sum((binomial(m-k+2,k-1)*binomial(n+1,k-1)*binomial(n-m+k-1,k-1)*binomial(2*n-2*k+4,2*m-4*k+5))/(binomial(2*k-2,k-1)*binomial(2*m-2*k+4,2*k-2)),k,1,(m+3)/2)/2;
%Y A338372 Cf. A001263, A008459
%K A338372 nonn,tabl
%O A338372 0,2
%A A338372 _Vladimir Kruchinin_, Oct 23 2020