A138983 a(n) = (n+1)-th term of the (n+1)-th inverse binomial transform of this sequence for n>=0.

1, 2, 6, 33, 241, 2391, 30903, 499000, 9804344, 230270387, 6364661087, 204142831017, 7508991442137, 313657014920304, 14753881974826196, 775751424297987671, 45294591976852153687, 2919681469388967044215

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

O.g.f. satisfies: a(n-1) = [x^n] A( x/(1+n*x) )/(1+n*x) for n>=1 with a(0)=1.

Example

If the successive inverse binomial transforms are placed in a table,
then we see that the diagonal consists of this sequence shift right:
n=0:[(1),2,6,33,241,2391,30903,499000,9804344,230270387,...];
n=1:[1, (1),3,20,138,1465,19591,325497,6558907,157672912,...];
n=2:[1,0, (2),13,73,949,12511,214938,4430056,108883779,...];
n=3:[1,-1,3, (6),34,693,7683,145147,3012155,75811514,...];
n=4:[1,-2,6,-7, (33),547,3967,104868,2029432,53365459,...];
n=5:[1,-3,11,-32,106, (241),1423,87045,1273819,38606532,...];
n=6:[1,-4,18,-75,313,-735, (2391),77062,613352,30170147,...];
n=7:[1,-5,27,-142,738,-3251,13291, (30903),131611,27084334,...];
n=8:[1,-6,38,-239,1489,-8657,47143,-161808, (499000),25380339,...];
n=9:[1,-7,51,-372,2698,-18903,126807,-734927,3716987, (9804344),...].

Prog

(PARI) {a(n)=local(A=[1]); for(k=1, n, A=concat(A, 0); A[k+1]=A[k]-polcoeff(subst(Ser(A), x, x/(1+k*x+x*O(x^k)))/(1+k*x), k)); A[n+1]}

Crossrefs

Sequence in context: A280769 A127114 A138909 * A121774 A209238 A053042

Adjacent sequences: A138980 A138981 A138982 * A138984 A138985 A138986

Keyword

nonn

Author

Paul D. Hanna, Apr 05 2008

Status

approved