A solid state lamp with efficient heat sink arrangement. To provide adequate cooling utilizing a defined form factor, such as that of the A-lamp incandescent bulb, the interior volume is used more efficiently. As one example, a solid state lamp employs a heat sink with inward facing fins. Solid state light sources, such as light emitting diodes (LEDs), are mounted on the exterior of the heat sink. An air path for convective flow is established through the center of the lamp.