A102055 Column 1 of A102054, the matrix inverse of A060083 (Euler polynomials).

1, 2, 1, 4, -13, 142, -1931, 36296, -893273, 27927346, -1081725559, 50861556172, -2854289486309, 188475382997654, -14467150771771043, 1277417937676246672, -128570745743431055281, 14632875988040732946106, -1869882665740777942166543, 266593648798424693540514836

Offset: 0

Author

Paul D. Hanna, Dec 28 2004

Keywords

• sign

Comments

1-a(n+1) equals the n-th partial sum of the Genocchi numbers (A001469).

Crossrefs

Cf. A001469, A060083, A102054, A102056.

Programs

PARI

{a(n)=local(M=matrix(n+2,n+2));M[1,1]=1;if(n>0,M[2,1]=1;M[2,2]=1); for(r=3,n+2, for(c=1,r,M[r,c]=if(c==1,M[r-1,1], if(c==r,1,M[r,c]=M[r-1,c]-((matrix(r-1,r-1,i,j,M[i,j]))^-1)[r-1,c-1])))); return(if(n==0,1,M[n+2,2]))}

Formula

a(n) = 1 - Sum_{k=1, n} A001469(k) for n>0, with a(0)=1.

This sequence's twin numbers are given in A133135. - Paul Curtz, Aug 07 2008