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

0,3

Links

Table of n, a(n) for n=0..23.

Formula

G.f. satisfies: A(x) = 1 + x*sum_{n>=0} x^n*A(x/(1-n*x))/(1-n*x).

Example

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,...

Prog

(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))}

Crossrefs

Cf. A095788.

Sequence in context: A202059 A350492 A014322 * A368636 A060996 A134378

Adjacent sequences: A095145 A095146 A095147 * A095149 A095150 A095151

Keyword

nonn

Author

Paul D. Hanna, Jun 05 2004

Status

approved