The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A111531 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A111531

Row 4 of table A111528.
(history; published version)

#37 by Joerg Arndt at Tue Jan 21 00:04:45 EST 2020

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proposed

approved

#36 by Jon E. Schoenfield at Mon Jan 20 23:01:56 EST 2020

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editing

proposed

#35 by Jon E. Schoenfield at Mon Jan 20 23:01:53 EST 2020

FORMULA

G.f.: (1/4)*Loglog(Sum_{n>=0} (n+3)!/3!*x^n) = Sum_{n>=1} a(n)*x^n/n.

G.f.: A(x) = 1/(1 + 4*x - 5*x/(1 + 5*x - 6*x/(1 + 6*x - ... (continued fraction).

a(n) = Sum_{k, =0<=k<=..n} 4^(n-k)*A089949(n,k) . - Philippe Deléham, Oct 16 2006

G.f.: G(0)/2, where G(k) = 1 + 1/(1 - x*(k+1)/(x*(k-1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 05 2013

A(x) satisfies the Riccati equation x^2*A'(x) + 4*x*A^2(x) - (1 + 3*x)*A(x) + 1 = 0.

EXAMPLE

(1/4)*Log(log(1 + 4*x + 20*x^2 + 120*x^3 + ... + (n+3)!/3!)*x^n + ...)

= x + 6/2*x^2 + 46/3*x^3 + 416/4*x^4 + 4256/5*x^5 + ...

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approved

editing

#34 by Susanna Cuyler at Tue Oct 01 09:50:49 EDT 2019

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proposed

approved

#33 by Jean-François Alcover at Tue Oct 01 05:18:08 EDT 2019

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editing

proposed

#32 by Jean-François Alcover at Tue Oct 01 05:18:03 EDT 2019

MATHEMATICA

T[n_, k_] := T[n, k] = Which[n<0 || k<0, 0, k==0 || k==1, 1, n==0, k!, True, (T[n-1, k+1]-T[n-1, k])/n-Sum[T[n, j]*T[n-1, k-j], {j, 1, k-1}]];

a[n_] := T[4, n];

a /@ Range[0, 19] (* Jean-François Alcover, Oct 01 2019 *)

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approved

editing

#31 by N. J. A. Sloane at Thu Jul 12 00:35:39 EDT 2018

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proposed

approved

#30 by Michel Marcus at Thu Jul 12 00:22:36 EDT 2018

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editing

proposed

#29 by Michel Marcus at Thu Jul 12 00:22:33 EDT 2018

FORMULA

a(n) = Sum_{k, 0<=k<=n}4^(n-k)*A089949(n,k) . - Philippe Deléham, Oct 16 2006

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proposed

editing

#28 by Michael De Vlieger at Wed Jul 11 21:38:08 EDT 2018

STATUS

editing

proposed