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 A269943 Triangle read by rows, T(n,k) = ((-1)^k*(2*n)!/4^k)*P[n,k](1/((2*n-1)*(2*n))) where P is the inverse P-transform, for n>=0 and 0<=k<=n. 0
 1, 0, 1, 0, 2, 6, 0, 16, 60, 90, 0, 288, 1176, 2520, 2520, 0, 9216, 39360, 98280, 151200, 113400, 0, 460800, 2023296, 5504400, 10311840, 12474000, 7484400, 0, 33177600, 148442112, 426666240, 896575680, 1362160800, 1362160800, 681080400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The P-transform is defined in the link. Compare also the Sage implementation below. LINKS Peter Luschny, The P-transform. FORMULA T(n,1) = 2^(n-1)*(n-1)!^2 (cf. A055546) for n>=1. T(n,n) = (2*n)!/2^n = A000680(n). EXAMPLE Triangle starts: [1] [0, 1] [0, 2, 6] [0, 16, 60, 90] [0, 288, 1176, 2520, 2520] [0, 9216, 39360, 98280, 151200, 113400] [0, 460800, 2023296, 5504400, 10311840, 12474000, 7484400] PROG (Sage) # The function PtransMatrix is defined in A269941: eul = lambda n: 1/((2*n-1)*(2*n)) norm = lambda n, k: (-1)^k*factorial(2*n)/4^k PtransMatrix(7, eul, norm, inverse = True) CROSSREFS Cf. A000680, A055546. Sequence in context: A131105 A321713 A057635 * A243015 A139717 A285119 Adjacent sequences:  A269940 A269941 A269942 * A269944 A269945 A269946 KEYWORD nonn,tabl AUTHOR Peter Luschny, Mar 27 2016 STATUS approved

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