A107104 Absolute row sums of triangle A107102, which is the matrix inverse of A100862.

1, 2, 6, 26, 154, 1182, 11254, 128522, 1715802, 26251118, 453132214, 8714516538, 184817376154, 4285657717694, 107880712446966, 2929921866938858, 85399256991014746, 2659096654189212558, 88091786616208073398

Offset: 0

Author

Paul D. Hanna, May 21 2005

Keywords

• nonn

Links

• W. Mlotkowski, A. Romanowicz, A family of sequences of binomial type, Probability and Mathematical Statistics, Vol. 33, Fasc. 2 (2013), pp. 401-408.

Crossrefs

Cf. A100862, A043301, A107102, A107103.

Programs

PARI

a(n)=if(n==0,1,2^n*sum(k=0,n-1,(n+k-1)!/(n-k-1)!/k!/4^k))

PARI

a(n)=local(X=x+x*O(x^n),Y=y+y*O(y^n)); sum(k=0,n,abs((matrix(n+1,n+1,m,j,if(m>=j, (m-1)!*polcoeff(polcoeff(exp(X+Y*X^2/2+X*Y),m-1,x),j-1,y)))^-1)[n+1,k+1]))

Formula

a(n) = 2*A043301(n-1) = 2^n*Sum_{k=0..n-1}(n+k-1)!/(n-k-1)!/k!/4^k for n>0, with a(0) = 1.