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 A354402 a(n) is the numerator of Sum_{k=1..n} (-1)^(k+1) / (k*k!). 3
 1, 3, 29, 229, 5737, 8603, 210781, 26979863, 728456581, 3642282779, 440716217519, 1762864869691, 297924162982399, 260683642609331, 15641018556560861, 4004100750479565401, 1157185116888594641129, 31243998155992054970143, 11279083334313131850347743, 112790833343131318500567523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..20. FORMULA Numerators of coefficients in expansion of (gamma + log(x) - Ei(-x)) / (1 - x), x > 0. EXAMPLE 1, 3/4, 29/36, 229/288, 5737/7200, 8603/10800, 210781/264600, ... MATHEMATICA Table[Sum[(-1)^(k + 1)/(k k!), {k, 1, n}], {n, 1, 20}] // Numerator nmax = 20; Assuming[x > 0, CoefficientList[Series[(EulerGamma + Log[x] - ExpIntegralEi[-x])/(1 - x), {x, 0, nmax}], x]] // Numerator // Rest PROG (PARI) a(n) = numerator(sum(k=1, n, (-1)^(k+1)/(k*k!))); \\ Michel Marcus, May 26 2022 (Python) from math import factorial from fractions import Fraction def A354402(n): return sum(Fraction(1 if k & 1 else -1, k*factorial(k)) for k in range(1, n+1)).numerator # Chai Wah Wu, May 27 2022 CROSSREFS Cf. A001563, A053557, A061354, A103816, A120265, A239069, A353545, A354404 (denominators). Sequence in context: A220548 A153825 A201490 * A135163 A074366 A037791 Adjacent sequences: A354399 A354400 A354401 * A354403 A354404 A354405 KEYWORD nonn,frac AUTHOR Ilya Gutkovskiy, May 25 2022 STATUS approved

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Last modified July 20 09:18 EDT 2024. Contains 374445 sequences. (Running on oeis4.)