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 A229032 Triangle T(n,k), 0 <= k <= n, read by rows, defined by T(n,k) = 4^k * C(n+1,2*k+1). 0
 1, 2, 0, 3, 4, 0, 4, 16, 0, 0, 5, 40, 16, 0, 0, 6, 80, 96, 0, 0, 0, 7, 140, 336, 64, 0, 0, 0, 8, 224, 896, 512, 0, 0, 0, 0, 9, 336, 2016, 2304, 256, 0, 0, 0, 0, 10, 480, 4032, 7680, 2560, 0, 0, 0, 0, 0, 11, 660, 7392, 21120, 14080, 1024, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row n is the sum of the convolution of A089627(p,i) with A089627(n-p,i), for p=0,1,...,n. LINKS Rui Duarte and António Guedes de Oliveira, A Famous Identity of Hajós in Terms of Sets, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.1. FORMULA T(n,k) = 4^k * C(n+1, 2*k+1). T(n,k) = sum(p=0..n, sum(i=0..k, C(p,i)*C(p-i, i)*C(n-p,k-i)*C(n-p-k+i, k-i))). T(n,k) = A085841(n/2,k), if n is even. T(n,k) = 2^k * A105070(n,k). EXAMPLE Triangle: 1 2, 0 3, 4, 0 4, 16, 0, 0 5, 40, 16, 0, 0 6, 80, 96, 0, 0, 0 7, 140, 336, 64, 0, 0, 0 8, 224, 896, 512, 0, 0, 0, 0 9, 336, 2016, 2304, 256, 0, 0, 0, 0 10, 480, 4032, 7680, 2560, 0, 0, 0, 0, 0 11, 660, 7392, 21120, 14080, 1024, 0, 0, 0, 0, 0 CROSSREFS Sequence in context: A078436 A209705 A181289 * A117909 A261094 A091538 Adjacent sequences:  A229029 A229030 A229031 * A229033 A229034 A229035 KEYWORD nonn,tabl AUTHOR Rui Duarte and António Guedes de Oliveira, Sep 11 2013 STATUS approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)