The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A342186 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A342186

Triangle read by rows, matrix inverse of A139382.
(history; published version)

#40 by N. J. A. Sloane at Mon Feb 26 10:34:47 EST 2024

STATUS

proposed

approved

#39 by Fabian Pereyra at Thu Feb 08 09:43:11 EST 2024

STATUS

editing

proposed

#38 by Fabian Pereyra at Thu Feb 08 09:43:04 EST 2024

FORMULA

T(n,k) = Sum_{j=k..n} (-1)^(n-j)*2^binomial(n-j,2)*qBinomial(n,j,2)*binomial(j,k), where qBinomial(n,k,2) is A022166(n,k). - Fabian Pereyra, Feb 08 2024

STATUS

approved

editing

#37 by Peter Luschny at Tue Jun 28 00:24:05 EDT 2022

STATUS

editing

approved

#36 by Peter Luschny at Tue Jun 28 00:24:00 EDT 2022

MAPLE

A342186 := proc(n, k) if n = 1 and k = 1 then 1 elif k > n or k < 1 then 0 else

A342186(n-1, k-1) - (2^(n-1) - 1) * A342186(n-1, k) fi end:

for n from 1 to 8 do seq(A342186(n, k), k = 1..n) od; # Peter Luschny, Jun 28 2022

STATUS

approved

editing

#35 by Michael De Vlieger at Sun Jun 26 14:03:17 EDT 2022

STATUS

reviewed

approved

#34 by Wesley Ivan Hurt at Sun Jun 26 13:25:46 EDT 2022

STATUS

proposed

reviewed

#33 by Michel Marcus at Sun Jun 26 13:19:19 EDT 2022

STATUS

editing

proposed

#32 by Michel Marcus at Sun Jun 26 13:19:04 EDT 2022

PROG

(PARI) mat(nn) = my(m = matrix(nn, nn)); for (n=1, nn, for(k=1, nn, m[n, k] = if (n==1, if (k==1, 1, 0), if (k==1, 1, (2^k-1)*m[n-1, k] + m[n-1, k-1])); ); ); m; \\ A139382

STATUS

approved

editing

Discussion

Sun Jun 26

13:19

Michel Marcus: function return was missing

#31 by Wolfdieter Lang at Wed May 05 17:52:41 EDT 2021

STATUS

editing

approved