0,5

Row n equals column 0 of matrix product A136467^(n+1) for n>=0.

O.g.f. of row n: Sum_{k>=0} ((n+1)/2)^k*log(1 + 2^k*x)^k/k! = Sum_{k>=0} C((n+1)*2^(k-1), k)*x^k for n>=0.

1,1,1,4,70,4368,906192,621216192,1429702652400,11288510714272000,...;

1,2,6,56,1820,201376,74974368,94525795200,409663695276000,...;

1,3,15,220,10626,1712304,927048304,1708566412608,...;

1,4,28,560,35960,7624512,5423611200,13161885792000,...;

1,5,45,1140,91390,24040016,21193254160,63815149590720,...;

1,6,66,2024,194580,61124064,64300886496,231207760388736,...;

1,7,91,3276,367290,134153712,163995687856,685581099291712,...;

1,8,120,4960,635376,264566400,368532802176,1756185841659392,...; ...

Triangle A136467 begins:

1;

1,1;

1,4,1;

4,32,16,1;

70,848,576,64,1;

4368,75648,62208,9216,256,1;

906192,22313216,21169152,3792896,143360,1024,1;

621216192,21827627008,23212261376,4793434112,223215616,2228224,4096,1;

such that row n of A136462 equals column 0 of A136467^(n+1).

(PARI) {T(n, k)=binomial((n+1)*2^(k-1), k)} (PARI) /* T(n, k) = Coefficient of x^k in series: */ {T(n, k)=polcoeff(sum(i=0, k, ((n+1)/2)^i*log(1+2^i*x +x*O(x^k))^i/i!), k)}

Cf. rows: A136465, A014070, A136466, A101346; A136463 (diagonal); A136467.

Adjacent sequences: A136459 A136460 A136461 this_sequence A136463 A136464 A136465

Sequence in context: A123353 A056646 A056056 this_sequence A060517 A074662 A025243

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2007