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A297703 The Genocchi triangle read by rows, T(n,k) for n>=0 and 0<=k<=n.

%I A297703 #8 Jun 03 2022 10:06:36
%S A297703 1,1,1,2,3,3,8,14,17,17,56,104,138,155,155,608,1160,1608,1918,2073,
%T A297703 2073,9440,18272,25944,32008,36154,38227,38227,198272,387104,557664,
%U A297703 702280,814888,891342,929569,929569,5410688,10623104,15448416,19716064,23281432,26031912
%N A297703 The Genocchi triangle read by rows, T(n,k) for n>=0 and 0<=k<=n.
%e A297703 The triangle starts:
%e A297703 0: [     1]
%e A297703 1: [     1,      1]
%e A297703 2: [     2,      3,      3]
%e A297703 3: [     8,     14,     17,     17]
%e A297703 4: [    56,    104,    138,    155,    155]
%e A297703 5: [   608,   1160,   1608,   1918,   2073,   2073]
%e A297703 6: [  9440,  18272,  25944,  32008,  36154,  38227,  38227]
%e A297703 7: [198272, 387104, 557664, 702280, 814888, 891342, 929569, 929569]
%o A297703 (Julia)
%o A297703 function A297703Triangle(len::Int)
%o A297703     A = fill(BigInt(0), len+2); A[2] = 1
%o A297703     for n in 2:len+1
%o A297703         for k in n:-1:2 A[k] += A[k+1] end
%o A297703         for k in 2: 1:n A[k] += A[k-1] end
%o A297703         println(A[2:n])
%o A297703     end
%o A297703 end
%o A297703 println(A297703Triangle(9))
%o A297703 (Python)
%o A297703 from functools import cache
%o A297703 @cache
%o A297703 def T(n):  # returns row n
%o A297703     if n == 0: return [1]
%o A297703     row = [0] + T(n - 1) + [0]
%o A297703     for k in range(n, 0, -1): row[k] += row[k + 1]
%o A297703     for k in range(2, n + 2): row[k] += row[k - 1]
%o A297703     return row[1:]
%o A297703 for n in range(9): print(T(n))  # _Peter Luschny_, Jun 03 2022
%Y A297703 Row sums are A005439 with offset 0.
%Y A297703 T(n,0) = A005439 with A005439(0) = 1.
%Y A297703 T(n,n) = A110501 with offset 0.
%Y A297703 Cf. A001469, A014781, A099959, A226158.
%K A297703 nonn,tabl
%O A297703 0,4
%A A297703 _Peter Luschny_, Jan 03 2018