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A352250
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Expansion of e.g.f. 1 / (1 - x * sin(x)) (even powers only).
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2
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1, 2, 20, 486, 21944, 1591210, 169207092, 24808395262, 4796420822384, 1182349445882706, 361939981107422060, 134705596642758848806, 59900689507397744253096, 31365504832631796986962426, 19102102945852191813235300004, 13387748268024668296590660222030
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..15.
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FORMULA
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a(0) = 1; a(n) = 2 * Sum_{k=1..n} (-1)^(k+1) * binomial(2*n,2*k) * k * a(n-k).
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MATHEMATICA
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nmax = 30; Take[CoefficientList[Series[1/(1 - x Sin[x]), {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]
a[0] = 1; a[n_] := a[n] = 2 Sum[(-1)^(k + 1) Binomial[2 n, 2 k] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]
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PROG
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(PARI) my(x='x+O('x^40), v=Vec(serlaplace(1 /(1-x*sin(x))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Mar 10 2022
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CROSSREFS
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Cf. A000111, A000364, A009214, A205571, A210657, A302397, A352251, A352252.
Sequence in context: A274572 A292396 A274738 * A012816 A012340 A279839
Adjacent sequences: A352247 A352248 A352249 * A352251 A352252 A352253
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Mar 09 2022
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STATUS
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approved
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