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 A054766 a(n+2) = (2*n + 3)*a(n+1) + (n + 1)^2*a(n), a(0) = 1, a(1) = 0. 5
 1, 0, 1, 5, 44, 476, 6336, 99504, 1803024, 37019664, 849418560, 21539756160, 598194037440, 18056575823040, 588622339549440, 20609136708249600, 771323264354361600, 30729606721005830400, 1298448658633614566400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Numerators of the convergents of the generalized continued fraction expansion 4/Pi - 1 = [0; 1/3, 4/5, 9/7,..., n^2/(2*n + 1),...] = 1/(3 + 4/(5 + 9/(7 + ...))). The first 4 convergents are 1/3, 5/19, 44/160 and 476/1744. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..392 K. S. Brown, Integer Sequences Related To Pi FORMULA a(n) ~ (1 - Pi/4) * (1 + sqrt(2))^(n + 1/2) * n^n / (2^(1/4) * exp(n)). - Vaclav Kotesovec, Feb 18 2017 MATHEMATICA RecurrenceTable[{a[n+2] == (2*n+3)*a[n+1] + (n+1)^2*a[n], a[0] == 1, a[1] == 0}, a, {n, 0, 25}] (* Vaclav Kotesovec, Feb 18 2017 *) t={1, 0}; Do[AppendTo[t, (2(n-2)+3)*t[[-1]]+(n-1)^2*t[[-2]]], {n, 2, 18}]; t (* Indranil Ghosh, Feb 25 2017 *) CROSSREFS Cf. A012244, A054765. Sequence in context: A222508 A220841 A343425 * A252830 A301434 A232192 Adjacent sequences: A054763 A054764 A054765 * A054767 A054768 A054769 KEYWORD nonn,easy,frac AUTHOR N. J. A. Sloane, May 26 2000 EXTENSIONS More terms from James A. Sellers, May 27 2000 Definition expanded by Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008 Keyword frac added by Michel Marcus, Feb 25 2017 STATUS approved

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Last modified November 30 05:38 EST 2022. Contains 358431 sequences. (Running on oeis4.)