A113147
Row 6 of table A113143; equal to INVERT of 6-fold factorials shifted one place right.
Original entry on oeis.org
1, 1, 2, 10, 110, 1954, 47270, 1437562, 52531310, 2239259266, 109021857446, 5966767051354, 362558298692270, 24214789406313442, 1763062297639690790, 138975554045857840570, 11790733617760291994990, 1071215297856049456744642
Offset: 0
A(x) = 1 + x + 2*x^2 + 10*x^3 + 110*x^4 + 1954*x^5 +...
= 1/(1 - x - x^2 - 7*x^3 - 91*x^4 -...- A008542(n)*x^(n+1)
-...).
-
{a(n)=local(x=X+X*O(X^n)); A=1/(1-x-x^2*sum(j=0,n,x^j*prod(i=0,j,6*i+1)));return(polcoeff(A,n,X))}
A113148
Row 7 of table A113143; equal to INVERT of 7-fold factorials shifted one place right.
Original entry on oeis.org
1, 1, 2, 11, 141, 2928, 82597, 2925973, 124502114, 6179425823, 350316271761, 22326710345256, 1579953165170881, 122905129550802985, 10423661531476766834, 957176457621821573987, 94608465923392572536421
Offset: 0
A(x) = 1 + x + 2*x^2 + 11*x^3 + 141*x^4 + 2928*x^5 +...
= 1/(1 - x - x^2 - 8*x^3 - 120*x^4 -...- A045754(n)*x^(n+1)
-...).
-
{a(n)=local(x=X+X*O(X^n)); A=1/(1-x-x^2*sum(j=0,n,x^j*prod(i=0,j,7*i+1)));return(polcoeff(A,n,X))}
A113149
Row 8 of table A113143; equal to INVERT of 8-fold factorials shifted one place right.
Original entry on oeis.org
1, 1, 2, 12, 176, 4184, 134824, 5451528, 264710536, 14992543432, 969925065992, 70547721068232, 5697913588192520, 505926926171909576, 48979597517592503560, 5134435963996172979912, 579379155027833982679816
Offset: 0
A(x) = 1 + x + 2*x^2 + 12*x^3 + 176*x^4 + 4184*x^5 +...
= 1/(1 - x - x^2 - 9*x^3 - 153*x^4 -...- A045755(n)*x^(n+1)
-...).
-
{a(n)=local(x=X+X*O(X^n)); A=1/(1-x-x^2*sum(j=0,n,x^j*prod(i=0,j,8*i+1)));return(polcoeff(A,n,X))}