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

Author

Paul D. Hanna, Jun 05 2004

Keywords

• nonn

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

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).