cp's OEIS Frontend

A102472 Triangle read by rows. Let S(k) be the sequence defined by F(0)=0, F(1)=1, F(n-1) + (n+k)*F(n) = F(n+1). E.g. S(0) = 0, 1, 1, 3, 10, 43, 225, 1393, 9976, 81201, ... Then S(0), S(1), S(2), ... are written vertically, next to each other, with the initial term of each on the next row down.

%I A102472 #16 Jul 26 2023 21:12:00
%S A102472 1,1,1,3,2,1,10,7,3,1,43,30,13,4,1,225,157,68,21,5,1,1393,972,421,130,
%T A102472 31,6,1,9976,6961,3015,931,222,43,7,1,81201,56660,24541,7578,1807,350,
%U A102472 57,8,1,740785,516901,223884,69133,16485,3193,520,73,9,1
%N A102472 Triangle read by rows. Let S(k) be the sequence defined by F(0)=0, F(1)=1, F(n-1) + (n+k)*F(n) = F(n+1). E.g. S(0) = 0, 1, 1, 3, 10, 43, 225, 1393, 9976, 81201, ... Then S(0), S(1), S(2), ... are written vertically, next to each other, with the initial term of each on the next row down.
%C A102472 T(n,1) = A001040(n); T(n,k) = A058294(n,n+k-1), k = 1..n. - _Reinhard Zumkeller_, Sep 14 2014
%C A102472 This triangle results when the first column is removed from A062323. - _Georg Fischer_, Jul 26 2023
%H A102472 Reinhard Zumkeller, <a href="/A102472/b102472.txt">Table of n, a(n) for n = 1..7875</a>
%e A102472 Triangle begins:
%e A102472 [1] 1;
%e A102472 [2] 1, 1;
%e A102472 [3] 3, 2, 1;
%e A102472 [4] 10, 7, 3, 1;
%e A102472 [5] 43, 30, 13, 4, 1;
%e A102472 [6] 225, 157, 68, 21, 5, 1;
%e A102472 [7] 1393, 972, 421, 130, 31, 6, 1;
%e A102472 [8] 9976, 6961, 3015, 931, 222, 43, 7, 1;
%o A102472 (Haskell)
%o A102472 a102472 n k = a102472_tabl !! (n-1) !! (k-1)
%o A102472 a102472_row n = a102472_tabl !! (n-1)
%o A102472 a102472_tabl = map reverse a102473_tabl
%o A102472 -- _Reinhard Zumkeller_, Sep 14 2014
%Y A102472 Mirror image of triangle in A102473.
%Y A102472 Cf. A001040, A058294, A062323, A247365 (central terms).
%K A102472 easy,nonn,tabl
%O A102472 1,4
%A A102472 _Russell Walsmith_, Jan 09 2005
%E A102472 Entry revised by _N. J. A. Sloane_, Jul 09 2005