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 A305532 Expansion of 1/(1 - x/(1 - 1*2*x/(1 - 2*3*x/(1 - 3*4*x/(1 - 4*5*x/(1 - ...)))))), a continued fraction. 3
 1, 1, 3, 21, 315, 8613, 372123, 23145957, 1951467291, 213852190437, 29523337936155, 5011258121042661, 1025542423300379931, 248988579422292953829, 70752815796279635539227, 23261468728483619098626789, 8760705555494801063319729435, 3747001028007419861036996070117 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Invert transform of tangent numbers (A000182). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..243 N. J. A. Sloane, Transforms FORMULA a(n) ~ 2^(4*n + 1) * n^(2*n - 1/2) / (exp(2*n) * Pi^(2*n - 1/2)). - Vaclav Kotesovec, Jun 08 2019 MAPLE b:= proc(x, y) option remember; `if`(y<0 or y>x, 0,      `if`(x=0, 1, max(1, y)*(b(x-1, y-1)+b(x-1, y+1))))     end: a:= n->  b(2*n, 0) : seq(a(n), n=0..22);  # Alois P. Heinz, Jun 08 2018 MATHEMATICA nmax = 17; CoefficientList[Series[1/(1 - x/(1 + ContinuedFractionK[-k (k + 1) x, 1, {k, 1, nmax}])), {x, 0, nmax}], x] nmax = 17; CoefficientList[Series[1/(1 - Sum[2 PolyGamma[2 k - 1, 1/2]/Pi^(2 k) x^k, {k, 1, nmax}]), {x, 0, nmax}], x] a[0] = 1; a[n_] := a[n] = Sum[2^(2 k) (2^(2 k) - 1) Abs[BernoulliB[2 k]]/(2 k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}] CROSSREFS Cf. A000182, A002378, A303943, A305533. Sequence in context: A208731 A158888 A331583 * A005329 A341471 A134528 Adjacent sequences:  A305529 A305530 A305531 * A305533 A305534 A305535 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jun 04 2018 STATUS approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)