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 A060556 Bisection of triangle A060098: odd-indexed members of column sequences of A060098 (not counting leading zeros). 5
 1, 1, 2, 1, 6, 3, 1, 12, 16, 4, 1, 20, 50, 32, 5, 1, 30, 120, 140, 55, 6, 1, 42, 245, 448, 316, 86, 7, 1, 56, 448, 1176, 1284, 622, 126, 8, 1, 72, 756, 2688, 4170, 3102, 1113, 176, 9, 1, 90, 1200, 5544, 11550, 12122 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums give A060557. Column sequences without leading zeros give for m=0..5: A000012 (powers of 1), A002378 = 2*A000217, A004320, 4*A040977, A060558, 2*A060559. Companion triangle (even-indexed members) A060102. With offset 1 for n and k, T(n,k) is the number of (1-2-3)-avoiding trapezoidal words of length n that contain n+1-k 1s. A trapezoidal word (following Riordan) is a sequence (a_1,a_2,...,a_n) of integers with 1 <= a_i <= 2i-1. For example, T(3,3)=3 counts 122, 132, 133 and T(4,2)=12 counts 1112, 1113, 1114, 1115, 1116, 1117, 1121, 1131, 1141, 1151, 1211, 1311. - David Callan, Aug 25 2009 LINKS FORMULA a(n, m)= A060098(2*n+1-m, m). G.f. for column m: (x^m)*Po(m+1, x)/(1-x)^(2*m+1), with Po(n, x) = Sum_{j=0..floor(n/2)} binomial(n, 2*j+1)*x^j (odd members of row n of Pascal triangle A007318). a(n, m) = Sum_{j=0..floor((m+1)/2)} binomial(n-j+m, 2*m)*binomial(m+1, 2*j+1), n >= m >= 0, otherwise zero. EXAMPLE {1}; {1,2}; {1,6,3}; {1,12,16,4}; ...; Po(3,x) = 3 + x. CROSSREFS Sequence in context: A016545 A142977 A120108 * A222969 A132813 A034898 Adjacent sequences:  A060553 A060554 A060555 * A060557 A060558 A060559 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang, Apr 06 2001 STATUS approved

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Last modified October 27 01:02 EDT 2020. Contains 338035 sequences. (Running on oeis4.)