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 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. 6
 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 (list; table; graph; refs; listen; history; text; internal format)
 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

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Last modified December 8 16:32 EST 2023. Contains 367680 sequences. (Running on oeis4.)