0,5

Row g.f.s satisfy: R(x,0) = 1 + x*R(x,1)^2, R(x,1) = 1 + 2x*R(x,2)^2,

R(x,2) = 1 + 3x*R(x,3)^2, R(x,3) = 1 + 4x*R(x,4)^2, ...

where the initial rows begin:

R(x,0):[1,1,4,28,276,3480,53232,955524,19672320,456803328,...];

R(x,1):[1,2,12,114,1440,22368,409248,8585088,202733760,...];

R(x,2):[1,3,24,288,4440,82080,1752000,42178800,1127335680,...];

R(x,3):[1,4,40,580,10560,226560,5532960,150570240,4501422240,...];

R(x,4):[1,5,60,1020,21420,523320,14399280,437433780,14479664640,...];

R(x,5):[1,6,84,1638,38976,1068480,32716992,1098069504,39896236800,...];

R(x,6):[1,7,112,2464,65520,1991808,67189248,2469837888,97765355520,..];

R(x,7):[1,8,144,3528,103680,3461760,127569600,5098406400,...];

R(x,8):[1,9,180,4860,156420,5690520,227470320,9821970180,...];

R(x,9):[1,10,220,6490,227040,8939040,385265760,17875608960,..].

(PARI) {T(n, k)=local(A=1+(n+k+1)*x); for(j=0, k, A=1+(n+k+1-j)*x*A^2 +x*O(x^k)); polcoeff(A, k)}

Rows: A128318, A128571, A128572, A128573, A128574, A128575, A128576; A128577 (square of row 0), A128578 (main diagonal), A128579 (antidiagonal sums).

Adjacent sequences: A128567 A128568 A128569 this_sequence A128571 A128572 A128573

Sequence in context: A036560 A117297 A112973 this_sequence A143973 A011167 A014176

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 11 2007