The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A286718 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A286718

Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling1 triangle.
(history; published version)

#40 by Bruno Berselli at Fri Nov 16 04:53:43 EST 2018

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reviewed

approved

#39 by Peter Luschny at Fri Nov 16 03:22:08 EST 2018

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reviewed

#38 by Michel Marcus at Thu Nov 15 04:26:17 EST 2018

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proposed

#37 by Michel Marcus at Thu Nov 15 04:26:05 EST 2018

COMMENTS

The inverse of the Sheffer triangular matrix S2[3,1] = A282629 is the Sheffer matrix S1[3,1] = (1/(1 + x)^(1/3), log(1 + x)/3) with rational elements S1[3,1](n, k) = (-1)^(n-m)*T(n, k)/3^n. - Wolfdieter Lang, Nov 15 2018

FORMULA

Recurrence for row polynomials is R(n, x) = (x+1)*R(n-1, x+3), with R(0, x) = 1.

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#36 by Wolfdieter Lang at Thu Nov 15 04:20:58 EST 2018

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#35 by Wolfdieter Lang at Thu Nov 15 04:12:38 EST 2018

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editing

#34 by Bruno Berselli at Wed Jun 20 08:06:34 EDT 2018

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proposed

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#33 by Jean-François Alcover at Wed Jun 20 07:57:45 EDT 2018

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#32 by Jean-François Alcover at Wed Jun 20 07:57:36 EDT 2018

MATHEMATICA

T[n_ /; n >= 1, k_] /; 0 <= k <= n := T[n, k] = T[n-1, k-1] + (3*n-2)* T[n-1, k]; T[_, -1] = 0; T[0, 0] = 1; T[n_, k_] /; n<k = 0;

Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 20 2018 *)

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editing

#31 by N. J. A. Sloane at Sat Dec 16 15:14:16 EST 2017

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proposed

approved