cp's OEIS Frontend

A095148 Shifts left under antidiagonal sums of the table (A095788) of iterated binomial transforms of this sequence.

%I A095148 #3 Mar 30 2012 18:36:40
%S A095148 1,1,2,5,14,44,155,605,2584,11956,59461,315841,1782354,10638166,
%T A095148 66900149,441811845,3055188944,22065583000,166064430497,1299663352309,
%U A095148 10557811907818,88874221415746,774053270905621,6965452960952961
%N A095148 Shifts left under antidiagonal sums of the table (A095788) of iterated binomial transforms of this sequence.
%F A095148 G.f. satisfies: A(x) = 1 + x*sum_{n>=0} x^n*A(x/(1-n*x))/(1-n*x).
%e A095148 From the table (A095788) of iterated binomial transforms of this sequence, the antidiagonal sums form this sequence shift left:
%e A095148 1,1,2,5,14,44,155,605,2584,11956,59461,...
%e A095148 1,2,5,15,51,190,766,3329,15553,77822,...
%e A095148 1,3,10,37,150,656,3059,15111,78840,...
%e A095148 1,4,17,77,371,1892,10154,57077,334993,...
%e A095148 1,5,26,141,798,4708,28891,183953,1212664,...
%e A095148 1,6,37,235,1539,10394,72350,518505,3821409,...
%e A095148 1,7,50,365,2726,20840,163091,1306139,10699288,...
%e A095148 1,8,65,537,4515,38656,337114,2994701,27094705,...
%e A095148 1,9,82,757,7086,67292,648539,6344517,63004248,...
%e A095148 1,10,101,1031,10643,111158,1175006,12573713,...
%o A095148 (PARI) {a(n)=local(A);if(n<0,0,A=1+x+x*O(x^n);for(i=1,n+1,A=sum(k=0,n+1,x^k*subst(A,x,x/(1-k*x))/(1-k*x));A=1+x*A);polcoeff(A,n))}
%Y A095148 Cf. A095788.
%K A095148 nonn
%O A095148 0,3
%A A095148 _Paul D. Hanna_, Jun 05 2004