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A095148 Shifts left under antidiagonal sums of the table (A095788) of iterated binomial transforms of this sequence. 2
1, 1, 2, 5, 14, 44, 155, 605, 2584, 11956, 59461, 315841, 1782354, 10638166, 66900149, 441811845, 3055188944, 22065583000, 166064430497, 1299663352309, 10557811907818, 88874221415746, 774053270905621, 6965452960952961 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 05 2004
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)