A155810 Triangle, read by rows, where g.f.: A(x,y) = exp( Sum_{n>=1} (2^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.

1, 2, 1, 10, 6, 1, 188, 82, 14, 1, 16774, 4452, 490, 30, 1, 6745436, 1074934, 71108, 2602, 62, 1, 11466849412, 1082704500, 43173414, 951300, 13002, 126, 1, 80444398636280, 4411700155252, 104251164804, 1387446246, 11470404, 62538, 254, 1, 2306003967992402758, 72146891831948808, 989785148972932, 7803708940836, 38993810694, 129076164, 292810, 510, 1, 268654794629082985019564, 4724816968764733073446, 36967624172237518088, 169140002768370820, 500466007443108, 1001353593606, 1382564804, 1343434, 1022, 1

Offset

0,2

Comments

More generally, for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.

Links

Table of n, a(n) for n=0..54.

Formula

G.f.: A(x,y) = Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k.

Example

G.f.: A(x,y) = 1 + (2 + y)x + (10 + 6y + y^2)x^2 + (188 + 82y + 14y^2 + y^3)x^3 +...
Triangle begins:
1;
2, 1;
10, 6, 1;
188, 82, 14, 1;
16774, 4452, 490, 30, 1;
6745436, 1074934, 71108, 2602, 62, 1;
11466849412, 1082704500, 43173414, 951300, 13002, 126, 1;
80444398636280, 4411700155252, 104251164804, 1387446246, 11470404, 62538, 254, 1;
2306003967992402758, 72146891831948808, 989785148972932, 7803708940836, 38993810694, 129076164, 292810, 510, 1;
268654794629082985019564, 4724816968764733073446, 36967624172237518088, 169140002768370820, 500466007443108, 1001353593606, 1382564804, 1343434, 1022, 1; ...

Prog

(PARI) {T(n, k)=polcoeff(polcoeff(exp(sum(m=1, n+1, (2^m+y)^m*x^m/m)+x*O(x^n)), n, x), k, y)}
for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))

Crossrefs

Cf. A155200 (column 0), A155201 (row sums), A155811 (column 1).

Sequence in context: A319373 A143172 A004747 * A324246 A225470 A081099

Adjacent sequences: A155807 A155808 A155809 * A155811 A155812 A155813

Keyword

nonn,tabl

Author

Paul D. Hanna, Feb 04 2009

Status

approved