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%I #10 May 25 2018 08:27:26
%S 2,14,2,38,24,2,70,184,2,118,648,256,2,198,1656,2240,2,342,3752,9728,
%T 2560,2,614,8152,31168,25600,2,1142,17544,86784,132096,24576,2,2182,
%U 37816,225728,504320,278528,2,4246,81768,566784,1649152,1662976,229376,2,8358,177048,1393600,4945920,7335936,2916352
%N Triangle read by rows: T(n,k) = number of Ringel ladders of order n and genus k.
%H Esther Hunt Tesar, <a href="https://doi.org/10.1016/S0012-365X(99)00250-2">Genus distribution of Ringel ladders</a>, Discrete Mathematics 216.1-3 (2000): 235-252.
%e Triangle begins:
%e 2, 14,
%e 2, 38, 24,
%e 2, 70, 184,
%e 2, 118, 648, 256,
%e 2, 198, 1656, 2240,
%e 2, 342, 3752, 9728, 2560,
%e 2, 614, 8152, 31168, 25600,
%e ...
%o (PARI) T(n, k) = 2^(3*k+1)*binomial(n-k, k) + 2^(3*k)*binomial(n-k, k-1) + (2^(n+k) - 2^(3*k-3))*binomial(n-k+1, k-2) + (2^(n+k+1) - 2^(3*k-2))*binomial(n-k+1, k-1);
%o tabf(nn) = {for(n=1, nn, for(k=0, ceil((n+1)/2), print1(T(n,k), ", "); ); print();); }; \\ _Michel Marcus_, May 24 2018
%K nonn,tabf
%O 1,1
%A _N. J. A. Sloane_, Feb 02 2018
%E Corrected and extended by _Michel Marcus_, May 24 2018
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