cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A132007 Triangle, read by rows, where T(n,k) = T(n,k-1) + n*T(n-1,k-1) for n>0 and k>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1.

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%I A132007 #11 Dec 15 2017 13:45:45
%S A132007 1,1,2,2,4,8,8,14,26,50,50,82,138,242,442,442,692,1102,1792,3002,5212,
%T A132007 5212,7864,12016,18628,29380,47392,78664,78664,115148,170196,254308,
%U A132007 384704,590364,922108,1472756,1472756,2102068,3023252,4384820,6419284
%N A132007 Triangle, read by rows, where T(n,k) = T(n,k-1) + n*T(n-1,k-1) for n>0 and k>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1.
%C A132007 Column 0 and main diagonal (offset) equals A110083.
%H A132007 G. C. Greubel, <a href="/A132007/b132007.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A132007 T(n+1,0) = Sum_{k=0..n} (n!/k!)*C(n,k)*T(k,0) for n>=0 with T(0,0)=1.
%e A132007 Triangle begins:
%e A132007 1;
%e A132007 1, 2;
%e A132007 2, 4, 8;
%e A132007 8, 14, 26, 50;
%e A132007 50, 82, 138, 242, 442;
%e A132007 442, 692, 1102, 1792, 3002, 5212;
%e A132007 5212, 7864, 12016, 18628, 29380, 47392, 78664;
%e A132007 78664, 115148, 170196, 254308, 384704, 590364, 922108, 1472756;
%e A132007 1472756, 2102068, 3023252, 4384820, 6419284, 9496916, 14219828, 21596692, 33378740; ...
%t A132007 T[n_, k_] := T[n, k] = If[k < 0 || n < k, 0, If[n == 0 && k == 0, 1, If[k == 0, T[n - 1, n - 1], T[n, k - 1] + n*T[n - 1, k - 1]]]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Dec 15 2017 *)
%o A132007 (PARI) T(n,k)=if(k<0 || n<k,0,if(n==0 && k==0,1,if(k==0,T(n-1,n-1),T(n,k-1)+n*T(n-1,k-1))))
%Y A132007 Cf. A110083 (column 0); A132008 (row sums).
%K A132007 nonn,tabl
%O A132007 0,3
%A A132007 _Paul D. Hanna_, Aug 07 2007