cp's OEIS Frontend

A034850 Triangular array formed by taking every other term of Pascal's triangle.

%I A034850 #18 Feb 24 2018 09:23:55
%S A034850 1,1,2,1,3,1,6,1,5,10,1,6,20,6,1,21,35,7,1,28,70,28,1,9,84,126,36,1,
%T A034850 10,120,252,120,10,1,55,330,462,165,11,1,66,495,924,495,66,1,13,286,
%U A034850 1287,1716,715,78,1,14,364,2002,3432,2002,364,14,1,105,1365,5005,6435
%N A034850 Triangular array formed by taking every other term of Pascal's triangle.
%H A034850 G. C. Greubel, <a href="/A034850/b034850.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%H A034850 D. Dumont and J. Zeng, <a href="http://math.univ-lyon1.fr/homes-www/zeng/public_html/paper/publication.html">Polynômes d'Euler et les fractions continues de Stieltjes-Rogers</a>, preprint 1996.
%H A034850 D. Dumont and J. Zeng, <a href="https://doi.org/10.1023/A:1009759202242">Polynômes d'Euler et les fractions continues de Stieltjes-Rogers</a>, Ramanujan J. 2 (1998) 3, 387-410.
%F A034850 a(n) = A007318(2n) if both are regarded as integer sequences. - _Michael Somos_, Feb 11 2004
%e A034850 Triangle begins:
%e A034850   1;
%e A034850   1;
%e A034850   2;
%e A034850   1,  3;
%e A034850   1,  6,  1;
%e A034850   5, 10,  1;
%e A034850   6, 20,  6;
%e A034850   1, 21, 35,  7;
%t A034850 Table[If[k < 0 || k > (Floor[n/4] + Floor[(n + 1)/4]), 0, Binomial[n, 2*k + Mod[Floor[(n + 1)/2], 2]]], {n, 0, 20}, {k, 0, (Floor[n/4] + Floor[(n + 1)/4])}] // Flatten (* _G. C. Greubel_, Feb 23 2018 *)
%o A034850 (PARI) {T(n, k) = if( k<0 || k>n\4 + (n+1)\4, 0, binomial(n, 2*k + (n+1)\2%2))}; /* _Michael Somos_, Feb 11 2004 */
%Y A034850 Cf. A007318, A034839.
%K A034850 nonn,easy,tabf
%O A034850 0,3
%A A034850 _N. J. A. Sloane_