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A026944
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E.g.f. is inverse function to y -> integral from 0 to y of exp(-s^2).
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1
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1, 2, 28, 1016, 69904, 7796768, 1282366912, 291885678464, 87844207042816, 33775227494400512, 16152024497964817408, 9402833148376976193536, 6546848699382209957269504, 5372168190357763804164005888, 5130820073307731596716765724672, 5642704273822755928641583754215424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The generating function is odd, so this list contains only the nonzero coefficients in the Taylor expansion.
a(n) = A002067(n) * 2^{n-1}.
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LINKS
| D. Dominici, Nested derivatives: A simple method for computing series expansions of inverse functions. arXiv:math/0501052v2 [math.CA]
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FORMULA
| Nonzero constant terms of the polynomials in t defined by P_1=1, P_{n+1}=P'n+2*n*t*P_n; E.g.f. = (1/2*sqrt(Pi)*erf)^{-1}(x)
E.g.f. A(x) satisfies the differential equation A'(x)=exp(A(x)^2) [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Jan 22 2011]
Let D denote the operator g(x) -> d/dx(exp(x^2)*g(x)). Then a(n) = D^(2*n-2)(1) evaluated at x = 0. See [Dominici, Example 11]. - Peter Bala, Sep 08 2011
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PROG
| (PARI) v=Vec(serlaplace(serreverse(intformal(exp(-x^2)))));
vector(#v\2, n, v[2*n-1]) /* show terms */
/* Demonstration of Kruchinin's differential equation: */
default(seriesprecision, 55); /* that many terms */
A=serreverse(intformal(exp(-x^2))); /* e.g.f. */
deriv(A)-exp(A^2) /* gives O(x^57), i.e., zero up to order */
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CROSSREFS
| Cf. A002067.
Sequence in context: A012725 A012756 A009403 * A113633 A186491 A009674
Adjacent sequences: A026941 A026942 A026943 * A026945 A026946 A026947
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KEYWORD
| nonn
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AUTHOR
| Frederic Chapoton (chapoton(AT)math.jussieu.fr), Mar 22 2000
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