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 A238801 Triangle T(n,k), read by rows, given by T(n,k) = C(n+1, k+1)*(1-(k mod 2)). 8
 1, 2, 0, 3, 0, 1, 4, 0, 4, 0, 5, 0, 10, 0, 1, 6, 0, 20, 0, 6, 0, 7, 0, 35, 0, 21, 0, 1, 8, 0, 56, 0, 56, 0, 8, 0, 9, 0, 84, 0, 126, 0, 36, 0, 1, 10, 0, 120, 0, 252, 0, 120, 0, 10, 0, 11, 0, 165, 0, 462, 0, 330, 0, 55, 0, 1, 12, 0, 220, 0, 792, 0, 792, 0, 220, 0, 12, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are powers of 2. LINKS G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened FORMULA G.f.: 1/((1+(y-1)*x)*(1-(y+1)*x)). T(n,k) = 2*T(n-1,k) + T(n-2,k-2) - T(n-2,k), T(0,0) = 1, T(1,0) = 2, T(1,1) = 0, T(n,k) = 0 if k<0 or if k>n. Sum_{k=0..n} T(n,k)*x^k = A000027(n+1), A000079(n), A015518(n+1), A003683(n+1), A079773(n+1), A051958(n+1), A080920(n+1), A053455(n), A160958(n+1) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively. EXAMPLE Triangle begins: 1; 2, 0; 3, 0, 1; 4, 0, 4, 0; 5, 0, 10, 0, 1; 6, 0, 20, 0, 6, 0; 7, 0, 35, 0, 21, 0, 1; 8, 0, 56, 0, 56, 0, 8, 0; 9, 0, 84, 0, 126, 0, 36, 0, 1; 10, 0, 120, 0, 252, 0, 120, 0, 10, 0; etc. MATHEMATICA Table[Binomial[n + 1, k + 1]*(1 - Mod[k , 2]), {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Nov 22 2017 *) PROG (PARI) T(n, k) = binomial(n+1, k+1)*(1-(k % 2)); tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Nov 23 2017 CROSSREFS Cf. Columns: A000027, A000292, A000389, A000580, A000582, A001288, A010966, A010968, A010970, A010972, A010974, A010976, A010980, A010982, A010984, A010986, A010988, A010990, A010992, A010994, A010996, A010998, A011000, A017713, A017715, A017717, A017719, A017721, A017723, A017725, A017727, A017729, A017731, A017733, A017735, A017737, A017739, A017741, A017743, A017745, A017747, A017749, A017751, A017753, A017755, A017757, A017759, A017761, A017763. Cf. A095704, A178616. Sequence in context: A035614 A212138 A133735 * A095704 A163496 A092241 Adjacent sequences:  A238798 A238799 A238800 * A238802 A238803 A238804 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Mar 05 2014 STATUS approved

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Last modified June 12 07:43 EDT 2021. Contains 344943 sequences. (Running on oeis4.)