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 A117435 Triangle related to exp(x)*cos(2*x). 4
 1, 0, 1, -4, 0, 1, 0, -12, 0, 1, 16, 0, -24, 0, 1, 0, 80, 0, -40, 0, 1, -64, 0, 240, 0, -60, 0, 1, 0, -448, 0, 560, 0, -84, 0, 1, 256, 0, -1792, 0, 1120, 0, -112, 0, 1, 0, 2304, 0, -5376, 0, 2016, 0, -144, 0, 1, -1024, 0, 11520, 0, -13440, 0, 3360, 0, -180, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Diagonals correspond to rows of A117438. LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA Number triangle whose k-th column has e.g.f. (x^k/k!)*cos(2x); T(n, k) = binomial(n,k) * (-4)^((n-k)/2) * (1+(-1)^(n-k))/2. Sum_{k=0..n} T(n, k) = A006495(n). Sum_{k=0..floor(n/2)} T(n-k, k) = i^n * ((1+(-1)^n)/2) * (2*floor(n/2) + 1). - G. C. Greubel, Jun 01 2021 EXAMPLE Triangle begins: 1; 0, 1; -4, 0, 1; 0, -12, 0, 1; 16, 0, -24, 0, 1; 0, 80, 0, -40, 0, 1; -64, 0, 240, 0, -60, 0, 1; MATHEMATICA T[n_, k_]:= Binomial[n, k]*(2*I)^(n-k)*(1+(-1)^(n+k))/2; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 01 2021 *) PROG (Sage) flatten([[binomial(n, k)*(2*i)^(n-k)*(1+(-1)^(n+k))/2 for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 01 2021 CROSSREFS Cf. A006495 (row sums), A117411, A117436 (inverse), A117438. Sequence in context: A046781 A244530 A271424 * A282252 A268367 A117436 Adjacent sequences: A117432 A117433 A117434 * A117436 A117437 A117438 KEYWORD easy,sign,tabl AUTHOR Paul Barry, Mar 16 2006 STATUS approved

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Last modified February 20 20:16 EST 2024. Contains 370217 sequences. (Running on oeis4.)