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

0,2

Links

Table of n, a(n) for n=0..18.

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

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.

Prog

(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]))

Crossrefs

Cf. A100862, A043301, A107102, A107103.

Sequence in context: A159602 A032271 A205502 * A141761 A355206 A242574

Adjacent sequences: A107101 A107102 A107103 * A107105 A107106 A107107

Keyword

nonn

Author

Paul D. Hanna, May 21 2005

Status

approved