A089469 a(n+1) = the n-th term of the n-th binomial transform.

1, 1, 2, 10, 82, 946, 14246, 267974, 6117202, 166015698, 5273053710, 193534712510, 8119820921626, 385777848702394, 20583872009571798, 1224407374239009622, 80669343513439179922, 5852864801437926734482, 465237079520383362585598

Offset: 0

Author

Paul D. Hanna, Nov 08 2003

Keywords

• nonn

Comments

Form a square array where the n-th row is the n-th binomial transform of this sequence, starting with this sequence in the zeroth row; then the diagonal of the square array so formed is this sequence shifted 1 place left.

Examples

			Note the diagonal in the array of iterated binomial transforms:
[_1,1,2,10,82,946,14246,267974,..]
[1,_2,5,20,139,1482,21389,390832,..]
[1,3,_10,42,258,2438,32854,577362,..]
[1,4,17,_82,499,4264,52361,869270,..]
[1,5,26,146,_946,7770,87350,1346062,..]
[1,6,37,240,1707,_14246,151501,2159484,..]
[1,7,50,370,2914,25582,_267974,3588122,..]
[1,8,65,542,4723,44388,473369,_6117202,..]
		

Crossrefs

Cf. A071207, A088956.

Programs

PARI

{L=20; a=[1]; for(i=1,L,b=a; for(n=0,length(a)-1, b[n+1]=sum(k=0,n,a[k+1]*binomial(n,k)*n^(n-k)); ); a=concat(1,b); ); for(j=1,L,print1(a[j],","))}

Formula

a(n+1) = sum(k=0, n, a(k)*binomial(n, k)*n^(n-k))