Search: id:A112492
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%I A112492
%S A112492 1,1,1,1,3,1,1,7,11,1,1,15,85,50,1,1,31,575,1660,274,1,1,63,3661,46760,
%T A112492 48076,1764,1,1,127,22631,1217776,6998824,1942416,13068,1,1,255,137845,
%U A112492 30480800,929081776,1744835904,104587344,109584,1,1,511,833375
%N A112492 Triangle from inverse scaled Pochhammer symbols.
%C A112492 This expansion is based on the partial fraction identity: 1/product(x+j,
               j=1..m)= (1 + sum(((-1)^j)*binomial(m,j)*x/(x+j),j=1..m))/m!, e.g., 
               p. 37 of the Ch. Jordan reference.
%C A112492 Another version of this triangle (without a column of 1's) is A008969.
%C A112492 The column sequences are, for m=1..10: A000012 (powers of 1), A000225, 
               A001240, A001241, A001242, A111886-A111888.
%D A112492 Charles Jordan, Calculus of Finite Differences, Chelsea, 1965.
%H A112492 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A112492.text">
               First 10 rows.</a>
%F A112492 G.f. for column m>=1: (x^m)/product(1-m!*x/j, j=1..m).
%F A112492 a(n, m)= -(m!^(n-m+1))*sum(((-1)^j)*binomial(m, j)/j^(n-m+1), j=1..m), 
               m>=1. a(n, m)=0 if n+1<m.
%Y A112492 Row sums give A111885.
%Y A112492 Sequence in context: A059328 A075440 A137470 this_sequence A049290 A147990 
               A134567
%Y A112492 Adjacent sequences: A112489 A112490 A112491 this_sequence A112493 A112494 
               A112495
%K A112492 nonn,easy,tabl
%O A112492 0,5
%A A112492 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Sep 12 2005

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