A297703 - OEIS

%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