A095148 Shifts left under antidiagonal sums of the table (A095788) of iterated binomial transforms of this sequence.
1, 1, 2, 5, 14, 44, 155, 605, 2584, 11956, 59461, 315841, 1782354, 10638166, 66900149, 441811845, 3055188944, 22065583000, 166064430497, 1299663352309, 10557811907818, 88874221415746, 774053270905621, 6965452960952961
Offset: 0
Keywords
Examples
From the table (A095788) of iterated binomial transforms of this sequence, the antidiagonal sums form this sequence shift left: 1,1,2,5,14,44,155,605,2584,11956,59461,... 1,2,5,15,51,190,766,3329,15553,77822,... 1,3,10,37,150,656,3059,15111,78840,... 1,4,17,77,371,1892,10154,57077,334993,... 1,5,26,141,798,4708,28891,183953,1212664,... 1,6,37,235,1539,10394,72350,518505,3821409,... 1,7,50,365,2726,20840,163091,1306139,10699288,... 1,8,65,537,4515,38656,337114,2994701,27094705,... 1,9,82,757,7086,67292,648539,6344517,63004248,... 1,10,101,1031,10643,111158,1175006,12573713,...
Crossrefs
Cf. A095788.
Programs
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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))}
Formula
G.f. satisfies: A(x) = 1 + x*sum_{n>=0} x^n*A(x/(1-n*x))/(1-n*x).