A075511 Sixth column of triangle A075497.

1, 42, 1064, 21168, 365232, 5743584, 84713728, 1193127936, 16239711488, 215394955776, 2800564795392, 35851775791104, 453374980255744, 5677724481773568, 70550796621971456, 871159544637161472

Offset

0,2

Comments

The e.g.f. given below is Sum_{m=0..5} A075513(6,m)*exp(2*(m+1)*x)/5!.

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = A075497(n+6, 6) = (2^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*2)^n/5!.

G.f.: 1/Product_{k=1..6} (1 - 2*k*x).

E.g.f.: (d^6/dx^6)(((exp(2*x)-1)/2)^6)/6! = (-exp(2*x) + 160*exp(4*x) - 2430*exp(6*x) + 10240*exp(8*x) - 15625*exp(10*x) + 7776*exp(12*x))/5!.

Crossrefs

Cf. A075510, A075512.

Sequence in context: A050988 A163741 A140404 * A016094 A004361 A264178

Adjacent sequences: A075508 A075509 A075510 * A075512 A075513 A075514

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved