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 A158785 Expansion of e.g.f.: exp(t*x)/(1 - x^2/t - t^3*x^3). 1
 1, 0, 1, 2, 0, 0, 1, 0, 6, 0, 0, 7, 24, 0, 0, 12, 0, 0, 25, 0, 120, 0, 0, 260, 0, 0, 61, 720, 0, 0, 360, 0, 0, 1470, 0, 0, 841, 0, 5040, 0, 0, 15960, 0, 0, 5082, 0, 0, 5251, 40320, 0, 0, 20160, 0, 0, 122640, 0, 0, 134456, 0, 0, 20497, 0, 362880, 0, 0, 1512000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Rows n = 0..50 of the irregular triangle, flattened FORMULA T(n, k) = coefficients of e.g.f.: t^floor(n/2)*exp(t*x)/(1 - x^2/t - t^3*x^3). From G. C. Greubel, Dec 05 2021: (Start) T(n, floor(n/2) + n) = A330044(n). T(n, 0) = A005359(n). T(n, 1) = A005212(n). (End) EXAMPLE Irregular triangle begins as:       1;       0,    1;       2,    0, 0,     1;       0,    6, 0,     0,     7;      24,    0, 0,    12,     0, 0,     25;       0,  120, 0,     0,   260, 0,      0,   61;     720,    0, 0,   360,     0, 0,   1470,    0, 0,    841;       0, 5040, 0,     0, 15960, 0,      0, 5082, 0,      0, 5251;   40320,    0, 0, 20160,     0, 0, 122640,    0, 0, 134456,    0, 0, 20497; MATHEMATICA Table[CoefficientList[Expand[t^Floor[n/2]*n!*SeriesCoefficient[Series[Exp[t*x]/(1 - x^2/t - t^3*x^3), {x, 0, 20}], n]], t], {n, 0, 10}]//Flatten PROG (Sage) f(x, t) = exp(t*x)/(1 - x^2/t - t^3*x^3) def A158785(n, k): return ( factorial(n)*t^(n//2)*( f(x, t) ).series(x, 20).list()[n] ).series(t, 2*n+1).list()[k] flatten([[A158785(n, k) for k in (0..n+(n//2))] for n in (0..10)]) # G. C. Greubel, Dec 05 2021 CROSSREFS Cf. A005212, A005359, A158706, A158757, A330044. Sequence in context: A347097 A339274 A335156 * A346243 A349916 A349342 Adjacent sequences:  A158782 A158783 A158784 * A158786 A158787 A158788 KEYWORD nonn,tabl,changed AUTHOR Roger L. Bagula, Mar 26 2009 EXTENSIONS Edited by G. C. Greubel, Dec 05 2021 STATUS approved

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Last modified December 9 07:53 EST 2021. Contains 349627 sequences. (Running on oeis4.)