%I #8 Jun 03 2022 10:06:36
%S 1,1,1,2,3,3,8,14,17,17,56,104,138,155,155,608,1160,1608,1918,2073,
%T 2073,9440,18272,25944,32008,36154,38227,38227,198272,387104,557664,
%U 702280,814888,891342,929569,929569,5410688,10623104,15448416,19716064,23281432,26031912
%N The Genocchi triangle read by rows, T(n,k) for n>=0 and 0<=k<=n.
%e The triangle starts:
%e 0: [ 1]
%e 1: [ 1, 1]
%e 2: [ 2, 3, 3]
%e 3: [ 8, 14, 17, 17]
%e 4: [ 56, 104, 138, 155, 155]
%e 5: [ 608, 1160, 1608, 1918, 2073, 2073]
%e 6: [ 9440, 18272, 25944, 32008, 36154, 38227, 38227]
%e 7: [198272, 387104, 557664, 702280, 814888, 891342, 929569, 929569]
%o (Julia)
%o function A297703Triangle(len::Int)
%o A = fill(BigInt(0), len+2); A[2] = 1
%o for n in 2:len+1
%o for k in n:-1:2 A[k] += A[k+1] end
%o for k in 2: 1:n A[k] += A[k-1] end
%o println(A[2:n])
%o end
%o end
%o println(A297703Triangle(9))
%o (Python)
%o from functools import cache
%o @cache
%o def T(n): # returns row n
%o if n == 0: return [1]
%o row = [0] + T(n - 1) + [0]
%o for k in range(n, 0, -1): row[k] += row[k + 1]
%o for k in range(2, n + 2): row[k] += row[k - 1]
%o return row[1:]
%o for n in range(9): print(T(n)) # _Peter Luschny_, Jun 03 2022
%Y Row sums are A005439 with offset 0.
%Y T(n,0) = A005439 with A005439(0) = 1.
%Y T(n,n) = A110501 with offset 0.
%Y Cf. A001469, A014781, A099959, A226158.
%K nonn,tabl
%O 0,4
%A _Peter Luschny_, Jan 03 2018