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A208898
A diagonal of rectangular table A208896: a(n) = A208896(n+2,n).
2
1, 1, 2, 9, 72, 880, 14946, 331177, 9157984, 305879724, 12036430600, 547226046939, 28298540270928, 1643380366183920, 106042236588594096, 7535372761616117625, 585204851983514095424, 49344635724104556446660, 4491848127809479571999928, 439231681095730953672503448
OFFSET
0,3
COMMENTS
The g.f. of row n, R(n,x), in the rectangular table A208896 satisfies:
(1) R(n,x) = 1 + x*R(n,x)^n * [d/dx x/R(n,x)] for n>=0.
(2) [x^k] R(n,x)^(k-n+1) = [x^k] R(n,x)^(k-n) for k>=2.
Thus the main diagonal in A208896 obeys: A208896(n,n) = 0 for n>=2.
FORMULA
a(n) is divisible by n for n>=1.
EXAMPLE
a(n)/n = [1,1,3,18,176,2491,47311,1144748,33986636,1203643060,...] for n>=1.
PROG
(PARI) {a(n)=local(ROW=1+x+x*O(x^n)); for(i=0, n, ROW=1+x*ROW^(n+2)*deriv(x/ROW)); polcoeff(ROW, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A240956 A038035 A133984 * A108995 A184358 A132843
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 03 2012
STATUS
approved